Pentavalent symmetric graphs admitting vertex-transitive non-abelian simple groups

A graph Gamma is said to be symmetric if its automorphism group Aut(Gamma) is transitive on the arc set of Gamma. Let G be a finite non-abelian simple group and let Gamma be a connected pentavalent symmetric graph with G <= Aut(Gamma). In this paper, we show that if G is transitive on the vertex set of Gamma, then either G a Aut(Gamma) or Aut(Gamma) contains a nonabelian simple normal subgroup T such that G <= T and (G, T) is one of 58 possible pairs of non-abelian simple groups. In particular, if G is transitive on the arc set of Gamma, then (G, T) is one of 17 possible pairs, and if G is regular on the vertex set of Gamma, then (G, T) is one of 13 possible pairs, which improves the result on pentavalent symmetric Cayley graph given by Fang, et al. (2011). (C) 2017 Elsevier Ltd. All rights reserved.