Dr. Veena Mathad M.Sc ,Ph.D - University of Mysore

31. Vertex Component domination in graphs, Indian Journal of Mathematics, 48(1)(2006) 57-62(with B. Janakiram and M. A. Davis).32. The double bondage number of a graph, Ultra Science, 19(2)M(2007) 439- 442(with K. M.Yogeesh).33. Complementary total domination in graphs, Journal of Discrete Mathematical Science andCryptography, 10(4)(2007)505-516(with B. Chaluvaraju).34. Fuzzy Covering and Fuzzy Neighbourhood set in Fuzzy Graphs, Ultra Science 19(3)M(2007)601-608(with Q. M. Mahioub).35. The nonsplit domination number of Fuzzy graphs, Bull. Pure Appl. Math. 1(2)(2007) 200-207(with Q. M. Mahioub).36. The Double domination number of fuzzy graphs Journal of Applied Mathematical Analysisand Applications, 3(2) (2007) 97-104(with Q. M.Mahioub).37. On the number of minimum independent dominating sets in paths and cycles, Journal ofApplied Mathematical Analysis and Applications, 3(2)(2007) 155-169(with K. M. Yogeesh).38. Disjoint perfect domination number of a graph, Journal of Applied Mathematical Analysisand Applications, 3(2)(2007) 171-179(with B. Sharada).39. On independent neighbourhood and Coloring graphs, Advances in Theoretical and appliedMathematics, 2(2007) 117-122(with S. Ghobadi).40. Partially balanced incomplete block designs arising from minimum efficient dominating setsof a graphs, Bull. Pure Appl. Math. 2(1)(2008) 47-56(with B. Sharada).41. Inverse dominating set in Fuzzy graphs Proce. Of the Jangjeon Mathematical Society,11(1)(2008) 75-81(with S. Ghobadi and Q. M. Mahioub).42. Nomatically Cocritical Graphs, Ultra Science 20(1)M(2008) 205-208(with S. Ghobadi and K.M. Yogeesha).43. The Split domination number of fuzzy graphs, Far East Journal of Appl. Maths 30(1)(2008)125-132(with Q. M. Mahioub).44. The Split edge domination number of a graph, Far East J. of Appl. Maths. 30(1)(2008) 93-100.(with K. M. Yogeesha and S. Ghobadi).45. The Nomatic number problem in interval graphs, Far East J. of Appl. Maths, 30(2)(2008)235-244(with S. Ghobadi).46. Roman edge domination in graphs,Proc. Nat. Acad. Sci. Lett. (79)(2009) 45-50,(with B.Chaluvaraju and J. P. Srivastava).46. Swithing equivalence in symmetric n-Sigraphs-II,J. Orissa Math. Soc. 27(2)(2009)-(tonappear)(with R. Rangarajan and P. Siva Kota Reddy).47. The block perfect domination number of a graph,Advances and applications in DiscreteMathematics 4(2), (2009), 161-168,(with S. R. Ramachandra).

Books Published:1 Discrete Mathematics,No. of Ph. D's guided - awarded : 9No. of Ph. D's guided - in progress : 6

Dr. Chandrashekar AdigaM.Sc ,Ph.DDesignation : Professor of MathematicsEmail id : cadiga@maths.uni-mysore.ac.in, c_adiga@hotmail.comPhone Number : 9448888276/0821-2419830Area of Specialization : Special Functions, Number Theory, Partition Theory,Discrete Mathematics and Graph Theory.Research Area : Special Functions, Number Theory, Partition Theory, DiscreteMathematics and Graph Theory.No of Publications: 93List of Publications :INTERNATIONAL:1. simple proof for finite double series representations for the Bernoulli, Euler and TangentNumbers., Int.J.Math.Edu.Sci,Technol. (U.K.) vol.14 Nos. 5(1983) 652-654. C.Adiga(with S.Bhargava)2. On some Continued fraction identities of Srinivasa Ramanujan, Proc.Amer,Math.Soc.Vol.92 No.1 (1984) 13-18.C.Adiga (with S.Bhargava).3. Two generalizations of Ramanujan's continued fraction identities,Lecture Notes inMathematics. Springer-Verlag, Vol.1122,(1984) 56-62 C.Adiga (with S.Bhargava).4. Chapter 16 of Ramanujan's Second Note Book: Theta functions and Q.Series .Mem.Amer,Math. Soc. Vol.53 Vol.315(1985) 1-85 C.Adiga (with B.C.Berndt, S.Bhargava& G.N.Watson)5. On two elliptic θ- function identities stated by Srinivasa RamanujanInt.J.Math.Edu.Sci,Technol.(U.K.)Vol.18 No.2 (1987)318-320 C.Adiga (with S.Bhargava)6. Simple proofs of Jacobi's two and four square theorems. Int.J.Math.Edu.Sci,Technol.(U.K.) Vol.18 No.2 (1987)318-320 C.Adiga (with S.Bhargava )7. 7. An estimate of Ramanujan related to the greatest integer function.Bull AustralMath.Soc.Vol.44.No.1(1991) 149-154. C.Adiga (with S.Bhargava andD.D.Somashekara).8. A generalization of Shiokawa's Rational Approximations to Roger's-Ramanujan ContinuedFraction.Commentary Mathematici,Vol.41. No.2(1992) 125-134.C.Adiga (withS.Bhargava and D.D.Somashekara).9. On the representations of an integer as a sum of two or four triangularnumbers.Nihonkai Math. Hiyr,Vol.3 No.2 (1992) 125-131 C.Adiga.10. Ramanujan's 1 1 Summation and an interesting convolution identity.Bull Austral,Math.Soc.Vol.47,No.1(1993)155-162C.Adiga (with S.Bhargava and D.D.Somashekara).

11. On the representations of an integer as a sum of square and thrice asquare.Int.J.Math.Educ.Sci, Technol.Vol.24,No.3(1993)493-498. C.Adiga (withS.Bhargava and D.D.Somashekara).12. Three square theorem as an application on Andrew's identity. Fibonacci Quarterly,May(1993) 129-133. C.Adiga (with S.Bhargava and D.D.Somashekara).13. Jacobi's two square and four square theorems via. Roger's identity.TamkangJour.Math.Vol.25.No.1(1994)23-27.C.Adiga.14. A basic bilateral series summation formula and its applications.Integral Transforms andSpecial Functions, Vol.2 No.3 (1994) 165-184C.Adiga (with S.Bhargava ).15. A note on q-gamma and q-beta functions, Mathematica Balkanica, Vol.9 (1995) 35-41.C.Adiga .16. Ramanujan's summation formula and its applications,Proceedings of the InternationalConference on Transcedental Number Theory,Tokyo, 3-5 Dec(1996)8-26.C.Adiga.17. On some Rogers-Ramanujan type continued fraction identities,Mathematica Balkanica,New Series Vol.12,(1998) Nos. -2,37-45.C.Adiga (with D.D.Somashekara).18. On some new identities involving integrals of theta-functions,Advanced Studies incontemporary Mathematics V0l.3 o.2(2001)1-11.C.Adiga (with K.R.Vauki andM.S.Mahadeva Naika).19. Some new explicit evaluations of Ramanujan's Cubic Continued fraction,New ZealandJour. Math Vol.13(2002),109-114C.Adiga (with K.R.Vauki and M.S.Mahadeva Naika).20. Ramanujan's remarkable summation formula as a 2-parameter generalization of thequintuple product identity,Tamkang Jounal ofMathematics, Vol.33,No.3,(2002),285-288.C.Adiga (with S.Bhargava and M.S.Mahadeva Naika).21. A new class of modular equation akin to Ramanujan's P-Q eta-function identities andsome evaluations there from,Advanced Studies in contemporaryMathematics,(Kyungshang)Vol.5,1(2002).no.1,21-34.C.Adiga (with S.Bhargava andM.S.Mahadeva Naika).22. On a generalization of Sandor's functions Proc. JangjeonMath.Soc.Vol.5,No.2 (2002)121-124 .C.Adiga (with T.Kim).23. Common fixed points for sequence of mappings, Proc.Jangjeon Math. Soc. Vol.5,No.1(2002)21-34.C.Adiga (with iniswamy)24. A note on the values of (2k +1),Advanced studies in contemporary Mathematics, Vol.5, o.2(2002)163-166.C.Adiga(with L.C.Jang,T.Kim,Y.H.Kim,H.K.Pate and D.W.Park).24. Some theta function identities and new explicit evaluation of Rogers-Ramanujancontinued fraction, Tamsui Oxfor Jour. ath. Sci. Vol.18 No.1(2002)101-117.C.Adiga(with K.R.Vauki and K.Shivashankara).25. Continued fraction representations for theta functions,Proc. Jnagjeon Math. Soc. Vol.5,No.2(2002),115-120, NNTDM 9(2003),7-12.C.Adiga (with T.Kim,D-W.Parts, Y.S.Ro andL-C Jang)

26. A fixed point theorem on some non expansive type mappings on complete metric spaces.Fixed Point Theory and Applications Vol.4, (2003) 1-9. C.Adiga (with Giniswamy)27. On a continued fraction of Ramanujan, Tamsui Oxford Jour. Math. Sci. Vol.19, No.1(2003) 55-65.C.Adiga (with T.Kim)28. Modular equations in the theory of signature 3 and P-Q identities, Advanced Studies inContemporary Mathematics 7 (2003)No.1, 33-40.C.Adiga (with T.Kim and MahadevaNaika). On a q-analogue of Sandor's function .J. Inequal, Pure and AppliedMath.4(4)(2003)1-5 C.Adiga (with T.Kim ,D.D.Somashekara and Syed Noor Fathima ).29. On some transformation formulas for basic bilateral hypergeometric series, Proc. Of14 th International Conference of the Jangjeon Mathematical Society C.Adiga (withD.D.Somashekar and Syed Noor Fathima)30. A note on strongly multiplicative graphs, Discussions mathematicae Graph Theory,24(2004) 81-83. C.Adiga (with D.D.Somashekar and H.N.Ramaswamy)31. General relations between sums of squares and sums of triangular numbers, DiscreteMathematics C.Adiga (with Shaun Cooper and Jung Hun Han).32. Sums of products of generalized Bernoulli Numbers, Int. J. Math. Vol.5, No.1 (2004) 1-7.C. Adiga (With T. Kim).33. On a certain class of add-even partitions, Proc. Jangjeon Math. Soc. 7(2004) No 2, 89 -94. C. Adiga (with S. Bhargava and A.K.Agarwal)34. A Note on a Certain Continued fraction of Ramanujan Bull. Austral. Math. Soc. 70(2004), 489-497.C. Adiga (with N. Anitha).35. On transformation of basic bilateral series, Proc. Jangjeon Math. Soc, 8 (2005) No 1,107-112. C. Adiga (with D.D.Somashekara and S,N.Fathima).36. A new approach to Jacobi's theorems via Ramanujan's continued fractions, Bull.Austral. Math. Soc. Vol. 71(2005) 75-79. C. Adiga (with Jung Hun Han).37. A. General relation between sums of squares and sums of triangular numbers, Int. Jour.Number theory Vol. 1. No. 2 (2005) 175-182.C. Adiga (with Shaun Cooper and Jung HunHan).38. On the q-analogue of Gamma function and related inequalities I. Inequal. Pure andApplied Math Vol. 6 No 4 (2005) 1-8.C.Adiga (with Taekyun Kim).39. On some continued fractions of Ramanujan, Adv. Stud. Cont. Math., No.1, 12(2006),155-162. C.Adiga (with N. Anitha).40. On a reciprocity of Ramanujan, Tamsui Oxford J. Math. Sci., Vol. 22 No.1, (2006), 9-15.C.Adiga (with N. Anitha).41. An upper bound for maximum number of edges in a strongly multiplicative graph,Discussiones Mathematicae Graph Theory, 26(2006), 1-5. C.Adiga (with M. Smitha).42. On colorings of strongly multiplicative and strongly quotient graphs, Adv. Stud. Cont.Math., Vol. 13 No.2, (2006), 171-182. C.Adiga (with R. K. Zaferani).

NATIONAL:58. A basic hypergeometric transformation of Ramanujan and generalization. Indian J.Pure,Appl.Maths.Vol.17 No.3 (1986) 338-342.C.Adiga (with S.Bhargava).59. One some identities in the theory of elliptic functions found in the note books ofSrinivasa Ramanujan. Mysore University Journal vol.No.XXX (1987) 117-125.C.Adiga(with S.Bhargava).60. On some generalizations of Ramanujan's continued fraction identities. Proc.Ind. AcadSci. Vol.97 (1987) 31-43.C.Adiga (with S.Bhargava and D.D.Somashekara).61. On certain continued fractions related to 3 2 Basic Hypergeometric functions,Jour.Math.Sci,Vol.21, No.6(1987)613-629. C.Adiga (with S.Bhargava andD.D.Somashekara).62. Parity results deducible from certain theta function identities found in chapter ofRamanujan's second note book.Math.Student,Vol.57,Nos 1-4 (1989) 121-132. C.Adiga(with S.Bhargava and D.D.Somashekara).63. Some relations between infinite series and infinite products, Proceedings of thesymposium on Algebra and Number theory.Cochin,India, 27-28, July (1990) 23-29,C.Adiga (with S.Bhargava and D.D.Somashekara).64. A note on Ward's conjecture. Jour.Ind.Math.Soc.Vol.59,(1993)201-206. C.Adiga(withN.R.Mohan).65. A note on Euler's totient function .Jour.Ind.Math.Soc.Vol.62, Nos.1-4 (1996),169-174).C.Adiga (with H.N.Ramaswamy).66. Some interesting applications of Ramanujan's identities to representations of integersassums of squares. Presented at 62 nd Annual Conference of IMS held at IIT Kanpur during22-25 Dec.1996.C.Adiga (with S.Bhargava and D.D.Somashekara).67. A note on rational approximations Presented at 62 nd Annual Conference of IMS held AtIIT Kanpur during 22-25 Dec.1996. C.Adiga (with D.D.Somashekara and K.R.Vasuki).68. A note on rational approximations. Jour.Ind.Math.Soc.Vol.65, Nos.1-4(1998),181-189.C.Adiga (with K.R.Vasuki).69. Number of representations of an integer as a sum of a square and five times asquare.Jour.Ind.Math.Socl.Vol.65 Nos. 1-4(1998)249-251. C.Adiga (with S.Bhargava andD.D.Somashekara).70. Ramanujan's 1 1 summation and an interesting generalization of an identity of Jacobi.Indian Jour.Math.Socl.Vol.41 Nos.1-4(1999) 39-42. C.Adiga (with S.Bhargava andD.D.Somashekara).71. A fixed point theorem in four metric spaces, Jour.Nat and Phy, Sci,Vol.14,Nos. 1-2(2000)105-110.C.Adiga (with Giniswamy and S.L.Singh).72. Some explicit evaluations of theta-functions, Far East J,Math. Sci , Vol.2(4)(2000), 625-631.C.Adiga (with K.R.Vasuki ).

Yazoo River Basin nutrients

89. A generalization of Agarwal's Theorem, Ramanujan Math. Soc., Lecture Notes seriesNo.2, (2006), 15-17.C.Adiga (With N. Anitha and Jung Hun Han).90. General modular transformations for theta-functions, Indian J. Math. 49, No.2, (2007),239-251. C.Adiga (With M. S. Mahadeva Naika and Jung Hun Han).91. Strongly quotient graphs, South East Asian J. Math. And Math. Sc., 15 No.2 (2007), 119-127. C.Adiga (With R. K. Zaferani and M. Smitha).92. On a three variable reciprocity theorem, South East J. Math. And Math. Sc., Vol 6 No.2(2008), 57-61. C.Adiga (With P. S. Guruprasad).93. On modular relations for the functions analogous to Rogers-Ramanujan functions withapplications to partitions, South East J. Math. And Math. Sc., Vol 6 No.2, (2008), 131-144. C.Adiga (With K. R. Vasuki and B. R. Srivatsa Kumar)..PROCEEDINGS :Proceedings of the International Conference on The Works of Srinivasa Ramanujan (2001)C.Adiga (with D.D.Somashekara)..No. of Ph. D's guided - submitted : 1No. of Ph. D's guided - awarded : 6No. of Ph. D's guided - in progrees : 6

DR. D. D. SOMASHEKARAM.Sc ,Ph.DDesignation : Professor of MathematicsEmail id : dsomashekara@yahoo.comPhone Number : 9150057505/0821-2419831Area of Specialization : Special Functions, Number TheoryResearch Area : Special Functions, Number Theory, Discrete Mathematics andTheoryGraphResearch Guidance: Special Functions, Number Theory and Graph TheoryNo of Publications: 40List of Publications :International1. An estimate of Ramanujan related to the greatest integer function, Bull. Austral. Math.Soc., Vol. 44, No.1 (1991) 149-154 (with S. Bhargava and C. Adiga).2. A generalization of Shiokawa’s rational approximations to Rogers-Ramanujan continuedfraction, Comment. Math. Univ. Sancti Pauli, Vol. 41, No.2 (1992), 125-134 (with S.Bhargava and C. Adiga).3. Ramanujan’s remarkable summation and an interesting convolution identity, Bull.Austral. Math. Soc., Vol. 47 (1993), 155-162 (with S. Bhargava and C. Adiga).4. Three square theorem as an application of Andrews’ identity, Fibonacci Quart., Vol. 31(1993), 129-133 (with S. Bhargava and C. Adiga).5. Some eta-function identities deducible from Ramanujan’s 1 1 summation, J. Math. Anal.Appl., Vol. 176, No.2 (1993), 554-560 (with S. Bhargava).6. On the representations of an integer as a sum of a square and thrice a square, Int. J.Math. Ed. Sci. Tech. Vol. 24, No.3 (1993) 493-496 (with S. Bhargava and C. Adiga).7. On some Rogers – Ramanujan type continued fraction identities, Mathematica Balkanica,New Series Vol.12, Nos. 1 – 2 (1998), 37– 45 (with C. Adiga).8. On a q-analogue of Sandor’s Function, J. Inequal. Pure and Appl. Math. Vol.4, No. 4(2003) 1-5 (with C. Adiga, T. Kim and Syeda Noor Fathima).9. A note on strongly multiplicative graphs, Discussiones Mathematicae Graph Theory, Vol.24 (2004) 81-83 (with C. Adiga and H. N. Ramaswamy).10. On some generalizations of the Jacobi’s triple product identity, Proceedings of the 15 thInternational Conference of the Jangjeon Mathematical Society, Edts: S. H. Rim, L. C.Jang, T. Kim, H. K. Pak, (2004) 32-44.

11. On a generalization of Jacobi’s triple product identity and its applications, Adv. Stud.Contemp. Math., Vol. 9, No.2 (2004) 165-174 (with T. Kim and Syeda Noor Fathima).12. On transformations of basic bilateral series, Proc. Jangjeon Math. Soc., Vol.8, No.1(2005) 107-112 (with C. Adiga and Syeda Noor Fathima).13. Some q-gamma and q-beta function identities deducible from the reciprocity theorem ofRamanujan, Adv. Stud. Contemp. Math., Vol. 11, No. 2 (2005) 227-234 (with S.Bhargava and Syeda Noor Fathima).14. A new convolution identity deducible from the remarkable formula of Ramanujan,Taiwanese Jour. Math., Vol. 11, No. 2 (2007) 399 – 406 (with S. Bhargava and D.Mamta).15. On some arithmetic and real variable functions, Octogon Math. Mag., Vol. 15, No.1(2007) 63 – 73 (with Jozesf Sandor and D. Mamta).16. On some identities of Ramanujan found in his lost notebook, Adv. Stud. Contemp.Math., Vol. 16, No. 2 (2008) 171-180 (with D. Mamta).17. On Smarandachely harmonic graphs, Int. Jour. Math. Combin., Vol. 4 (2009) 75-83(with C. R. Veena).18. A note on three variable reciprocity theorem, Int. J. Pure Appl. Math (2010) (with D.Mamta).19. On the skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp. Math., Vol.20, No. 2 (2010) 261-269 (with C. Adiga, H. N. Ramaswamy and Z. Khoshbakht).20. On strong vertex graceful graphs. International Mathematical Forum, Vol. 5, No. 56,(2010) 2751-2757 (with C. R. Veena).21. On the three variable reciprocity theorem and its applications, The Aust. Jour. Math.Anal. and Appl. (AJMAA) , Vol. 9, No.1, Art.13(2012) 1-9 (With D. Mamta).22. On square sum labelings of graphs, Proc. Jangjeon Math. Soc., Vol. 15, No.1 (2012) 69-78 (with C.R.Veena).National:1. On some generalizations of Ramanujan’s continued fraction identities, Proc. Ind. Acad,Sci., Vol.97 (1987) 31-43 (with S. Bhargava and C. Adiga).2. On certain continued fractions related to 3 2 basic hypergeometric functions, Jour. Math.Sci., Vol. 21, No.6 (1987) 613 – 629 (with S. Bhargava and C. Adiga) .

3. Parity results deducible from certain theta function identities found in chapter 16 ofRamanujan’s second notebook, Math. Student, Vol. 57, Nos. 1-4 (1989) 121-132 (with S.Bhargava and C. Adiga).4. Some interesting applications of Ramanujan’s identities to representations of integers assums of squares. Presented at 62 nd Annual Conference of IMS, held at IIT, Kanpur, duringDecember 22 – 25, (1996) (with S. Bhargava and C.Adiga).5. Some relations between infinite series and infinite products, Proceedings of thesymposium on Algebra and Number Theory, Cochin, India, July 27-28, 1990, 23-29. (withS. Bhargava and C. Adiga)6. Number of representations of an integer as a sum of a square and five times a square,Jour. Ind. Math. Soc., Vol.65, Nos. 1-4 (1998), 249 – 251 (with S. Bhargava and C.Adiga) .7. Ramanujan’s 1 1 summation and an interesting generalization of an identity of Jacobi,Indian J. of Math., Vol. 41, No.1 (1999), 39-42 (with S. Bhargava and C. Adiga).8. Strongly * graphs, Mathematical Forum, Vol. 8, (1999-2000) 31-36. (with C. Adiga).9. Rogers – Ramanujan identities, continued fractions and their generalizations, SelectedTopics in Special Functions, Eds: R. P. Agarwal, H.L. Manocha and K. Srinivasa Rao(2001), 208-226.(with C. Adiga)10. Strongly multiplicative graphs, Challenges of the 21 st Century in Mathematics and its AlliedTopics: Ed: B. S. Kiranagi (2001), 232-235. (with C. Adiga and H. N. Ramaswamy).11. An interesting generalization of Jacobi’s triple product identity, Far East J.Math. Sci.(FJMS), Vol. 9, No. 3 (2003), 255-259. (with Syeda Noor Fathima)12. On strongly multiplicative graphs, South East Asian J. Math. and Math. Sci. vol.2 (2003)(with C.Adiga and H. N. Ramaswamy).13. On continued fraction expansions for the ratios of 2 2 , Indian J. of Math., Vol. 45,No.3(2003) 333-355 (with Syeda Noor Fathima)14. A new transformation for basic bilateral hypergeometric series, The Math. Student, Vol.74, Nos. 1 – 4 (2005) 11 – 29 (with S. Bhargava and Syeda Noor Fathima).15. On some continued fraction expansions for the ratios of 2 2 , Far East J. Math. Sci. (FJMS),Vol. 23, No. 1 (2006), 65-80 (with D. Mamta).16. Interesting generalizations of the additive analogues of the Euler minimum and maximumfunctions, South East Asian J. Math. and Math. Sci., Vol. 4, No. 2 (2006) 27 – 32 (withD. Mamta) .17. On a two variable reciprocity theorem of Ramanujan, Bull. Pure and Appl. Math., Vol. 5,No.1 (2011) ( with K. Narasimha Murthy).

18. On strongly harmonic graphs. Far East J. Math. Sci. (FJMS), (2012) (to appear) (with C. R.Veena).Books Published:Proceedings of The International Conference on The Works of SrinivasaRamanujan (2001) ( With C.Adiga )No. of Ph. D's guided - awarded : 2No. of Ph. D's guided - in progress : 3

DR. VASUKI K. R. M.Sc ,Ph.DDesignation : Associate ProfessorEmail id : Vasuki_kr@hotmail.comPhone Number :91-9916450314Area of Specialization : Number theory and Special functionResearch Area : Number theory and Special functionNo of Publications: 44List of Publications :International1. On Some New Identities Involving Integrals of Theta-functions, Advanced Studies inContemporary Mathematics, 3 (2001), 1-11, with C. Adiga and M. S. M. Naika.2. Some New Explicit Evaluations of Ramanujan's Cubic Continued Fractions, New Zealand Journalof Mathematics, 31 (2002), 109-114, with C. Adiga and M. S. M. Naika3. Some Theta Functions Identities and New Explicit Evaluations of Rogers RamanujanContinued Fractions, Tamsui Oxford, J. Mathematical Sciences, 18(1), (2002), 101-117,with C. Adiga and K. Shivashankara.4. A Note on Explicit Evaluation of Continued Fraction, Advanced Studies in ContemporaryMathematics, 9 (2004), 63-80, with T. G. Sreeramamurthy.5. A Note on P-Q Modular Equations, Tamsui Oxford Journal of Mathematical Sciences, 21(2)(2005), 109-120, with T. G. Sreeramamurthy.6. Certain New Ramanujan’s Schlafli Type Mixed Modular Equations, Journal of MathematicalAnalysis and Applications, 309 (2005), 238-255 with T. G. Sreeramamurthy.7. On Some Ramanujan’s Schalfli Type Modular Equations. Australian Journal of MathematicalAnalysis and Applications, 3(2) (2006), 1-8.8. Certain Identities for Ramanujan-Gollnitz-Gordon Continued Fraction, Journal of Comp. AndAppl. Math., 187 (2006), 87-95 with B. R Srivatsa Kumar.9. On 3 ψ 3 basic Bilateral Hypergeometric Series Summation Formulas, International J. Math.Combin., 4 (2009), 41-49, with G. Sharath.10. On a Continued Fraction of Order Six, Ann. Univ. Ferrara, 56 (2010), 77-89, with N. Bhaskar andG. Sharath.11. On a Continued Fraction of Order Twelve, Ukranian Mathematical J., 62(12) ( 2010),1609-1619,with Abdulrawf A. A. Kahtan, G. Sharath and C. Satish Kumar.

12. On a 2 ψ 2 Basic Bilateral Hypergeometric Series Summation Formula, International Math. Form,5(13-16), (2010), 745-753, with K. R. Rajanna.13. On Certain New Modular Relations for the Rogers-Ramanujan type functions of Order Twelve,Advanced Studies in Contemporary Mathematics, 20(3) (2010), 319-333, with P. S. Guruprasad.14. General Formulas for Evaluation of Singular Modulus of the Complete Elliptic Integral, AdvancedStudies in Contemporary Mathematics, 20(1) (2010), 29-56, with G. Sharath and N. Bhaskar.15. Two Modular Equations for Squares of the Cubic-Functions with Applications, Note diMatematica, 30(2) (2010), 61-72, with G. Sharath and K. R. Rajanna.16. On Certain Theta Function Identities Analogous to Ramanujan’s P-Q Eta-Function Identites,Applied Mathematics, 2(7) (2011), 874-882, with Abdulrawf A. A. Kahtan.17. On Some Identities of Ramanujan-Gollnitz-Gordon Continued Fraction, Notes in Number theoryand Discrete Mathematics, 17(4) (2011), 50-60, with G. Sharath and K. R. Rajanna.18. On the Series Expansion of the Ramanujan Cubic Continued Fraction, International J. Math.Combin., 4 (2011), 84-95, with Abdulrawf A. A. Kahtan and G. Sharath19. Some New Modular Relations for the Cubic Functions, Southeast Asian Bulletin of Mathematics (accepted), with C. Adiga and N. Bhaskar.National:1. A Note on Rational Approximation (Presented in the conference), with C. Adiga and D. D.Somashekara.2. A Note on Rational Approximations, Journal of Indian Math. Soc., Vol. 65, Nos. 1-4 (1998),181-189, with C. Adiga.3. On Some Continued Fractions Related to 2 2 Basic Bilateral Hypergeometric Seires,Mathematical Forum, 12, (1998), 31-43.4. W. N. Bailey's Basic Hypergeometric Series Summation Formula and its Applications, TheMath. Student, 68, (1999), 211-218.5. A Note on Explicit Evaluations of Products and Ratios of Class Invariants, MathematicalForum, Vol. XIII, 1999-2000, 45-56, with K. Shivashankar.6. Some Explicit Evaluations of Theta-Functions, Far East J. Math. Sci. (FJMS), 2(4) (2000),625-631, with C. Adiga.7. Some Evaluations of Rogers - Ramanujan Continued Fraction, Proceedings of the InternationalConference on The Works of Srinivasa Ramanujan, Eds: C. Adiga and D. D. Somashekara,July 1-2, 2000, 209-217, with M. S. M. Naika.8. Some New Explicit Evaluations of Ratios of Theta-Functions, Proc. Nat. Conf. On Challengesof the 21 th Century in Mathematics and its Allied topics, University of Mysore, Ed. B. S.Kirangi, 2001, 253-259, with M. S. M. Naika.9. On Some Ramanujan's P-Q Identities, Hardy-Ramanujan Journal, 24 (2001) 2-9, with M. S.M. Naika and H. S. Madhusudhan.

10. On Sums of Triangular Numbers, The Math. Student, 70, (2001), 185-190, with C. Adiga.11. On Some New Continued Fraction Expansions related to 2 1 Basic Hypergeometric Functions,Far East J. Math. Sci. (FJMS), 3(3) (2001), 435-443, with Shivashankara K.12. On Some Continued Fraction Expansions for the Ratios of 2 2 , Special Functions The AligarhBull. of Math., 21 (2002), 25-35 with C. Adiga and Remy Y. Denis.13. On Certain Continued Fractions Related to 2 2 Basic Bilateral Hypergeometric Functions,Indian J. Pure and Appl. Math., 33(10) (2002), 1563-1573, with H. S. Madhusudhan.14. On Ramanujan's Continued Fractions, Ganitha, 53(1) (2002), 81-88, with K. Shivashankar.15. Some New Values for the Roger’s-Ramanujan Continued Fraction, J. Indian Math. Soc., 70(2003), 87-95 with K. Shivashankar16. Some Evaluations of Ramanujan’s Cubic Continued Fraction, Indian J.pure appl. Math., 35(8)(2004), 1003-1025, with S. Bhargava and T. G. Sreeramamurthy.17. Evaluations of Ramanujan-Weber Class Invariant gn, Journal of Indian Math. Soc., 72(1-4)(2005), 115-127 with S. Bhargava and B. R Srivatsa Kumar.18. Evalutions of the Ramanujan-Gollnitz-Gordon Continued Fraction H(q) by Modular Equations,Indian Journal of Mathematics, 48(3) (2006), 275-300 with B. R. Srivatsa Kumar.19. A note on Ramanujan-Schlafli type mixed modular equations, South east Asian Journal ofMathematics and Mathematical Sciences, 5(1) (2006), 51-67 with B. R. Srivatsa Kumar.20. A New Identity for the Roger’s-Ramanujan Continued Fraction, Journal of AppliedMathematical Anal. And Appl., 2(1) (2006), 71-83 with S. R. Swamy.21. On Some Ramanujan’s P-Q Modular Equations, J. of Indian Math. Soc., 73 (2006), 131-143.22. On Certain Ramanujan-Weber type modular equations, J. of Indian Math. Soc, 75 (2008), 173-192.23. K. R. Vasuki, P. S. Guruprasad, G. Sharath and C. Chamaraju, On certain new continuedfractions related to 3 φ 2 basic hypergeometric functions, South east Asian Journal ofMathematics and Mathematical Sciences, accepted.24. K. R. Vasuki and C. Chamaraju, A Simple Proof of W. N. Baley’s 2 ψ 2 Bilateral BasicHypergeometric Series Transformation Formula, The Mathematics Student, accepted25. K. R. Vasuki and T. G. Sreeramurthy, A Note on Rational Approximation of a NewGeneralization of the Rogers-Ramanujan Continued Fraction, Mathematical Forum, acceptedBooks Published:No. of Ph. D's guided - awarded : 06No. of Ph. D's guided - in progress : 05

Dr. R. RANGARAJANM.Sc ,Ph.DDesignationEmail id: Associate professor: ranga@maths.uni-mysore.ac.in,rajra63@gmail.comPhone Number : 0821-2419829/9611109079Area of Specialization : Pade Approximation, Differential Equations,Graph TheoryResearch Area : MathematicsResearch Guidance : Recognised guide from 06-02-2001No. of Publications : 41List of Publication :International:1. A Novel Approximate Method for a Nonlinear Heat Transfer Problem,International J. of Math. Sci. & Engg. Appls., Vol. 5, No.1 (January, 2011),61-67 (with H. Muneer Basha).2. Switching Invariant Neighborhood Signed Graphs, Proceedings of the JangjeonMath. Soc. 14(2) (2011) 249-258 (with P. Siva Kota Reddy and M. S.Subramanya).3. Numerical-Analytic Methods for Nonlinear Diffusion Type Differential Equationsof Heat Transfer, Journal of the Indian Math. Soc., Vol. 77, No.s 1-4, (2010),159-166 (with H. Muneer Basha).4. The Edge C 4 Signed Graph of a Signed Graph, Southeast Asian Bulletin ofMathematics 34(6)(2010) 1077-1082 (with P. Siva Kota Reddy)5. A Result of Ramanujan and Brahmagupta Polynomials Described by a MatrixIdentity, International Journal of Mathematical Combinatorics, InternationalJ. Math. Combin. , Vol.3 (October 2010), 57-63.6. The H-Line Signed Graph of a Signed Graph, J.Math. Combin., Vol.2 (2010),37-43 (with P. Siva Kota Reddy and M. S. Subramanya).7. Notions of balance and consistency on symmetric n-marked graphs, Bul. Pure& Appl. Math, 3(1) (2009), 1-8 (with P. Siva Kota Reddy).8. Switching Equivalence in Symmetric n-Sigraphs, Adv. Stud. Comtemp. Math.18(1) (2009), 79-85 (with P. Siva Kota Reddy and M. S. Subramanya).9. Neighbourhood Signed Graphs, Southeast Asian Bulletin of Mathematics(2009)33: 1-10 (with M. S. Subramanya and P. Siva Kota Reddy)10. Global Analysis of Lotka-Volterra Predator-Prey Model with Intraspeciescompetition, Journal of Analysis and Computation, 4.1 (2008): 79-85 (withM.H. Rahmani Doust).11. Identity and Non-identity Graphs on n-Sigraphs, International J. of Math. Sci.& Engg. Appls. 2.3(2008):111-117 (with P. Siva Kota Reddy).12. Analysis of a Predator-Prey Model with Intraspecies Coexistence, Jour. ofUltra. Sci. Phy. Sci., 20 (3) (2008)819-824 (with M.H. Rahmani Doust).13. Notions of Balance in Symmetric n-Sigraphs, Proceedings of the JangjeonMath. Soc. 11(2) (2008)145-151 (with P. Siva Kota Reddy).14. A regular perturbation method for Fisher-Kolmogrov type PDEs, InternationalJournal of Physical Sciences, 19.3M (2007), 503-510 (with ChandraliBaishya).15. Perturbation and Painleve analysis for potential KdV and SSD equations,Journal of Mathematical Analysis and Applications, 3.1 (2007):7-14 (withChandrali Baishya).

16. A perturbation series solution for KdV-Burger equation, Journal ofMathematical Analysis and Applications, 3.1 (2007):15-21 (with ChandraliBaishya).17. Geometric models for multiplication of octonions and sedenions, Journal ofAnalysis and Computation, 3.2 (2007):147-152 (with B. Gayathri Devi).18. A nonlinear impulsive differential system, International Journal of PhysicalSciences, 19.2M (2007), 377-382 (with Hamood A.K. Alhaddad).19. A nonlinear impulsive integro-differential system I, Journal of Analysis andComputation, 2.2 (2006), 125-131 (with Hamood A.K. Alhaddad).20. A nonlinear impulsive integro-differential system II, Journal of Analysis andComputation, 2.2 (2006), 133-140 (with Hamood A.K. Alhaddad).21. A nonlinear impulsive integro-differential system with infinite memory,Journal of Science and Technology, 11.1 (2006), 13-18 (with Hamood A.K.Alhaddad).22. The Brahmagupta polynomials extended by generalized golden ratio, Journalof Mathematical Analysis and Applications, 1.2 (2005), 157-168 (withRangaswamy).23. Orthogonal polynomials of continued fractions and Brahmagupta polynomials,Journal of Mathematical Analysis and Applications, 1.2 (2005), 169-181 (withRangaswamy).24. Brahmagupta Polynomials Arising from the Skew-field of Quaternion, SouthEast Asian Journal of Mathematics and Mathematical Sciences,3.2 (2005),59-65 (with B. Gayathri Devi) .25. The Brahmagupta Polynomials in Two Complex Variables and theirConjugates, The Fibonacci Quarterly, 40.2 (2002), 161-169. (With H.S.Sudheer).26. The Brahmagupta Matrix and its Application to Tiling, in Special Functions,Proceedings of the International Workshop held at the City University ofHongkong, June 21-25, 1999. Edited by Charles Dunkl, Mourad Ismail andRoderick Wong. World Scientific, Hongkong (2000), 282-292 (with E.R.Suryanarayan).27. Continued Fraction Solutions of Matrix Riccati Equation, In: MathematicalTheory of Control (Proceedings of the International Conference) Edited by M.C. Joshi and A. V. Balakrishnan, Marcel Dekker, Inc. (1993), 1-10. (With P.Achuthan).28. On Regular C-fraction and General T-fraction Expansions for Ratios of BasicHypergeometric Series and Ramanujan-type Identities, Applied NumericalMathematics, 12 (1993), 297-313 (with P. Achuthan).29. On KdV Solitons and Pade’ Approximants, Jour. Math. Phy. Sci, 25(3) (1991),287-304 (with P. Achuthan and R. Narasimhan)30. On a Continued Fraction Representation of General Cauer Third Form, Jour.Math. Phy. Sci, 24(6) (1990), 369-380 (with P. Achuthan).National :1. Mathematical Modelling and Computational Aspects of Nonlinear HeatTransfer Problems, Proceedings of the National Conference on “Mathematical Modelling: A Socio-Scientific Approach”, Nov. 30, 2011,Tumkur University(2011).2. Application of Pade Approximation in solving certain Nonlinear PDEs,Proceedings of the National Seminar on “Analysis of Partial Differential

Equations”, Dec. 18-19, 2009, Ed. Prof. M. Subbiah, PondicherryUniversity, Puducherry, (2010),3. Switching equivalence in symmetric n-Sigraphs. II. J. Orissa Math.Soc. 28 (2009), no. 1-2, 1-12 (with P. Siva Kota Reddy and D.S.Nandappa) 66-79.4. Switching invariant 2-path Sigraphs, My Science Vol. 1 (1) (2008), 20-25(with P. Siva Kota Reddy and M. S. Subramanya).5. New Perturbation Series Solutions for Fisher’s Equation, Journal of theKarnataka University, SCIENCE, 43 (2001), 1-11.6. On a new norm with an important role in computational vedicmathematics, Proceedings of National Workshop on Computational VedicMathematics, ED. K. N. Balasubramanya Murthy and B. S. Ramesh, 39-46(2002).7. A Vedic-type Sutra for Approximate Value of N, Applied Science Periodical,4.3 (2002), 152-158. (With Rangaswamy).8. On circulant Matrices representing certain directed graphs and magicalsemi graphs, Proceedings of the National Seminar on Graph Theory, ED. T.Thrivikraman, S. Kuriokose and N. Kalayani Kutty, 145-151 (2002).9. Properties of Brahmagupta Polynomials with two Parameters, Proceedingsof the Third Annual Conference of the Society For Special Functions andtheir Applications, BHU, Varanasi March 4-6, 2002. Editors R.S.Pathak,A.K. Agarwal and M.A. Pathan. Society For Special Functions and theirApplications (2003), 57-69. (with E.R. Suryanarayan and Rangaswamy).10. A Continued Fraction Expansion of N Involving a Positive Rational Solutionof x 2 –N y 2 = -1, Challenges of the 21st century in Mathematics and itsAllied Topics, Proceedings of the National Seminar, University of Mysore,Mysore, February 2-3 2001, Ed. by B.S.Kiranagi University of Mysore(2001), 224-231. (With Rangaswamy).11. Sums of Reciprocals Diverging To Infinity Without Hitting Any Integer,Challenges of the 21st century in Mathematics and its Allied Topics,Proceedings of the National Seminar, University of Mysore, Mysore,February 2-3 2001, Ed. by B.S.Kiranagi University of Mysore (2001), 236-241. (With E. R. Suryanarayan).Books Published:KSOU Course ware, M.Sc Mathematics 2.4, Numerical Analysis, 2011.No. of Ph. D’s guided - awarded : 07No. of Ph. D’s guided - in progress : 06

DR. H. N. RAMASWAMYM.Sc ,Ph.DDesignation : Professor of MathematicsEmail id : hnrama@gmail.comPhone Number : 9449530045/0821-2419832Area of Specialization : Algebra, Number Theory and Graph Theory.Research Area : Algebraic theory of Quadratic Forms, Number theory and Graph TheoryNo of Publications: 10List of Publications :1. A note on Euler's totient function, Jour. Ind. Math. Soc. Vol. 62, Nos.1-4 (1996),169-174 (with C. Adiga).2. On the Number of Semiorderings over Formally Fields, in Algebra and ItsApplications: Proceedings of the International Conference on Algebra and itsApplications, AMU, Aligarh, Narosa Publishing House, (2001) 257- 263.3. Strongly Multiplicative graphs, in Challenges of the 21st Century in Mathematicsand its Allied Topics; Ed: B. S. Kiranagi (2001), 232-235 (with C. Adiga and D.D. Somashekara).4. On Strongly Multiplicative Graphs, South East Asian J.Math. and Math. Sc. Vol.2,No.1, 45-47, 2003 (with C. Adiga and D. D. Somashekara).5. A Note on Strongly Multiplicative Graphs, Discuss. Math. Graph Theory 24(2004), 81-83 (with C. Adiga and D. D. Somashekara).6. On S-isotropy and Bani-fields, Proceedings of the Jangjeon MathematicalSociety, 8, No.1, (2005) 65 – 72.7. A note on certain divisibility problem, International Journal of MathematicalAnalysis, Vol. 2, no. 21-24, (2008) (with C. Adiga).8. On the energy of unitary Cayley graphs, The Electronic Journal of Combinatorics,16 (2009), N24 (with C.R.Veena).9. On the Skew energy of some unitary Cayley digraphs, Adv. Stud. Contemp.Math. 20, No.2 (2010) 261-269 (with C. Adiga, D. D. Somashekara, and Z.Khoshbakht).10. On the Stufe, unit stufe and the Pythagoras number of the ring of

integers modulo n, Adv. Stud. Contemp. Math. 20(3) (2010) 273-288. (withSiddaramu).Book Published:1. Math Unlimited: Essays in MathematicsH.N.Ramaswamy, R.Sujatha, C.S.Yogananda (eds.)Science Publishers & C R C Press, 2012No. of Ph. D's guided - awarded : 2- in progress : 1