Graphs whose full automorphism group is a symmetric group

Abstract

We address the problem of describing all graphs T such that Aut T is a symmetric group, subject to certain restrictions on the sizes of the orbits of Aut T on vertices. As a corollary of our general results we obtain a classification of all graphs font) vertices with Aut T = Sn, where v < min{5n,½n(n-1)}. © 1988, Australian Mathematical Society. All rights reserved.