Motivated by the question of the relative complexities of the Graph
Isomorphism and the Graph Automorphism problems, we define and study
the modular graph automorphism problems. These are the decision
problems mod_k-GA which consist, for each k>1, of deciding whether
the number of automorphisms of a graph is divisible by k. The
mod_k-GA problems all turn out to be intermediate in difficulty
between Graph Automorphism and Graph Isomorphism.
We define an appropriate search version of mod_k-GA and design an
algorithm that polynomial-time reduces the mod_k-GA search problem to
the decision problem. Combining this algorithm with an IP protocol,
we obtain a randomized polynomial-time checker for mod_k-GA, for all
CitationArvind, V., Beigel, R., Lozano, A. "The Complexity of modular graph automorphism". 1998.
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