Fullerenes 1

Basic Relations in Polyhedra
• First theorems on graph counting (Euler ( Euler) 1,2
∑d ( dv dvdd
) = 2 2ee (1)
∑s ( sf sfss
) = 2 2ee (2)
where vv dd and ff ss denote vertices of degree d d and ss--sized sized faces,
respectively.
1. Euler, L. Solutio Problematis ad Geometriam Situs Pertinentis.
Comment. Acad. Sci. I. Petropolitanae 1736, 8, , 128-140. 128 140.
2. King, King,
R. B., Applications of Graph Theory and Topology in
Inorganic Cluster and Coordination Chemistry, Chemistry,
CRC Press, 1993.
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