The operation of switching a graph Γ with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set of graphs on a given vertex set, so we can talk about the automorphism group of a switching class of graphs. It might be thought that switching classes with many automo...

A function f of a graph is called a complete graph invariant if G ∼= H is equivalent to f(G) = f(H). If, in addition, f(G) is a graph isomorphic to G, then f is called a canonical form for graphs. Gurevich [6] proves that graphs have a polynomial-time computable canonical form exactly when they have a polynomial-time computable complete invariant. We extend this equivalence to the polylogarithm...