Normal forms for trivalent graphs and graphs of bounded valence

A function f is defined, mapping graphs with n vertices onto graphs with vertex set {1,...,n} . f(X) is isomorphic to X and X is isomorphic to Y iff f(X) &equil; f(Y). For each d, the restriction of f to graphs of valence d is computable in time O(nτ(d)) for a suitable integer τ(d). For d > 3, the proof uses a recent result of L. Babai, P.J. Cameron and P.P. Pálfy on the order of primitive groups with bounded composition factors; for the trivalent case a more elementary proof is presented.

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