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The main results of this paper are an O(n3) probabilistic algorithm and an O(n3 log n) deterministic algorithm that test whether two given trivalent graphs are isomorphic. In fact, the algorithms construct the set of all isomorphisms of the two graphs. Variants of these algorithms construct the set of all automorphisms of a trivalent graph. The algorithms make use of some new improved permutation...
Suppose we are given a set of generators for a group G of permutations of a colored set A. The color automorphism problem for G involves finding generators for the subgroup of G which stabilizes the color classes. Testing isomorphism of graphs of valence ≤ t is polynomial-time reducible to the color automorphism problem for groups with small simple sections. The algorithm for the latter problem involves...
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