On the full automorphism group of a graph

Abstract

While it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary we find that, whenG is ap-group with no homomorphism ontoZ p wrZ p , almost all Cayley graphs ofG have automorphism group isomorphic toG.

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Godsil, C.D. On the full automorphism group of a graph. Combinatorica 1, 243–256 (1981). https://doi.org/10.1007/BF02579330

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AMS subject classification (1980)

  • 05 C 25
  • 05 B 25