Cubic graphical regular representations of Ree groups

Abstract

A graphical regular representation of a group G is a Cayley graph of G whose full automorphism group is equal to the right regular permutation representation of G. In this paper, we prove that for Ree groups with q > 3, with probability tending to 1 as , a random involution y together with a fixed element x with order q – 1 gives rise to a cubic graphical regular representation of . A similar result involving a fixed element with order is also proved with the help of certain properties of given in [Leemans, D. Liebeck, M. W. (2017). Chiral polyhedra and finite simple groups. Bull. London Math. Soc. 49: 581–592].