J Austral Math Soc Ser A 44 pp46--63, 1988.

Graphs Whose Full Automorphism Group is a Symmetric Group

Martin W. Liebeck

Abstract

We address the problem of describing all graphs G such that Aut G is a symmetric group, subject to certain restrictions on the sizes of the orbits of Aut G on vertices. As a corollary of our general results, we obtain a classification of all graphs G on v vertices with Aut G @ S_n, where

v < min ì í î 5n,  1 2 n(n - 1) ü ý þ .

1980 AMS Subject Classification: 05C25

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Authors

Martin W. Liebeck

Department of Mathematics, Imperial College, London S.W.7, England.