Chicago Journal of Theoretical Computer Science

Volume 1999

Article 1

Published by MIT Press. Copyright 1999 Massachusetts Institute of Technology.

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On Finding the Number of Graph Automorphisms

Robert Beals (University of Arizona), Richard Chang (University of Maryland Baltimore County), William Gasarch (University of Maryland College Park) and Jacobo Torán (University of Ulm)
10 February 1999

In computational complexity theory, a function f is called b(n)-enumerable if there exists a polynomial-time function that can restrict the output of f(x) to one of b(n) possible values. This paper investigates #GA, the function that computes the number of automorphisms of an undirected graph, and GI, the set of pairs of isomorphic graphs. The results in this paper show the following connections between the enumerability of #GA and the computational complexity of GI.

  1. #GA is e^(O(sqrt(n log n)))-enumerable}.
  2. If #GA is polynomially enumerable, then GI in R.
  3. For epsilon < 1/2, if #GA is n^epsilon-enumerable, then GI in P.

DOI: 10.4086/cjtcs.1999.001
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Last modified: Wed Feb 24 15:51:38 CST 1999