A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF $\text{A}_{39}$. Issue 3 (11th January 2016)

• Record Type: Journal Article
• Authors: LING, BO; LOU, BEN GONG
• Is Part Of: Bulletin of the Australian Mathematical Society. Volume 93:Issue 3(2016)
• Page Start: 441
• Page End: 446
• Publication Date: 2016-01-11
• Subjects: primary 20B25, -- secondary 05C25, -- 20D06; normal Cayley graph, -- symmetric graph, -- automorphism group, -- finite simple group; Mathematics -- Societies, etc; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0004972715001513
• Languages: English
• ISSNs: 0004-9727

Abstract

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 $\text{A}_{40}$ .