Graph Isomorphism Testing Without Full Automorphism Group Computation∗

In this paper we present an algorithm for testing the isomorphism of two graphs. The algorithm works in three steps. First, it builds a sequence of partitions on the vertices of one of the graphs. Then, it looks for some automorphisms in that graph. Finally, it uses backtracking to try to find another sequence of partitions for the second graph that is compatible with that for the first graph. We compare the performance of an implementation of this algorithm with other isomorphism testing programs. For this purpose we have chosen nauty, that is the fastest program we know of (it works computing a canonical form of the graphs), and vf2 that uses a completely different approach which looks useful for certain types of graphs. Several types of graphs have been used for the tests in their directed and undirected versions. Our program is faster that the other two in some cases, and behaves more uniformly in all of them.