A General Method for Graph Isomorphism

Authors:
Gabriel Valiente
Affiliations:
-
Venue:
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Year:
2001

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Abstract

A general method is presented for testing graph isomorphism, which exploits those sufficient conditions that define linear orderings on the vertices of the graphs. The method yields simple and constructive, low-order polynomial graph isomorphism algorithms for classes of graphs which have a unique ordering, or a small (not necessarily bounded) number of different orderings. The general method is instantiated to several graph classes, including: interval graphs, outerplanar graphs, biconnected outerplanar graphs, and triconnected planar graphs. Although more efficient algorithms are known for isomorphism on some of these classes of graphs, the method can be applied to any class of graphs having a polynomial number of different orderings and an efficient algorithm for enumerating all these orderings.