On cubic Cayley graphs of finite simple groups

Authors:
Xin Gui Fang;Cai Heng Li;Jie Wang;Ming Yao Xu
Affiliations:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China;Department of Mathematics and Statistics, The University of Western Australia Perth, WA 6907, Australia;Department of Mathematics, Peking University, Beijing 100871, People's Republic of China;Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Venue:
Discrete Mathematics - Algebraic and topological methods in graph theory
Year:
2002

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Abstract

For a finite group G, a Cayley graph Cay(G,S) is said to be normal if the group GR of right translations on G is a normal subgroup of the full automorphism group of Cay(G,S). In this paper, we prove that, for most finite simple groups G, connected cubic Cayley graphs of G are all normal. Then we apply this result to study a problem related to isomorphisms of Cayley graphs, and a problem regarding graphical regular representations of finite simple groups. The proof of the main result depends on the classification of finite simple groups.