On the decomposition of connected graphs into their biconnected components

Details On the decomposition of connected graphs into their biconnected components On the decomposition of connected graphs into their biconnected components

2010-01-19

arxiv.org/abs/1001.3163v2

Mathematics

Combinatorics

Scientific paper

We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u, biconnected components from one with u-1 biconnected components. We use such map to extend the aforesaid result to connected or 2-edge connected graphs. The underlying algorithms are amenable to computer implementation.

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