The.Algorithm.Design.Manual.Springer-Verlag.1998

Articulation Vertices
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Articulation Vertices
Figure: An articulation vertex is the weakest point in the graph
Suppose you are a terrorist seeking to disrupt the telephone network. Which station in Figure should
you choose to blow up to cause the maximum amount of damage? An articulation vertex is a vertex of a
connected graph whose deletion disconnects the graph. Any graph that contains an articulation vertex is
inherently fragile, because deleting that single vertex causes a loss of connectivity.
In general, the connectivity of a graph is the smallest number of vertices whose deletion will disconnect
the graph. For graphs with an articulation vertex, the connectivity is one. Connectivity is an important
measure of robustness in network design, as discussed in catalog Section .
A simple application of either depth-first or breadth-first search suffices to find all the articulation
vertices in a graph in O(n (m+n)). For each vertex v, delete it and then do a BFS traversal of the
remaining graph to establish whether it is still connected. In fact, there is a clever O(n+m) algorithm that
tests all the vertices using only a single depth-first search. Additional information on edge and vertex
connectivity testing appears in Section .
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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