2-Arc-transitive hexavalent Cayley graphs on nonabelian simple groups. Issue 11 (19th August 2022) - Pan, Jiangmin; Wu, Cixuan; Zhang, Yingnan
Abstract: A plenty of contributions have been done on symmetric Cayley graphs on nonabelian simple groups, but the only known complete classification of such graphs with composite valency is of valency 4 (provided 2-arc-transitivity) by Fang et al. [Europ. J. Combin. 25 (2004), 1107–1116] and Du and Feng [Comm. Algebra 47 (2019), 4565–4574]. This naturally motivates this work for classifying 2-arc-transitive hexavalent Cayley graphs on nonabelian simple groups. It is proved that these graphs are either normal or ( A n, 2 ) -arc-transitive Cayley graphs on A n − 1 where n is among 11 specific numbers dividing 2 7 · 3 3 · 5 3 . A specific example is also constructed.