A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF $\text{A}_{39}$. Issue 3 (11th January 2016) - LING, BO; LOU, BEN GONG
Abstract : Zhou and Feng ['On symmetric graphs of valency five', Discrete Math.  310 (2010), 1725–1732] proved that all connected pentavalent 1-transitive Cayley graphs of finite nonabelian simple groups are normal. We construct an example of a nonnormal 2-arc transitive pentavalent symmetric Cayley graph on the alternating group $\text{A}_{39}$ . Furthermore, we show that the full automorphism group of this graph is isomorphic to the alternating group $\text{A}_{40}$ .