Abstract
For a finite group G, a Cayley graph Cay( G, S) is said to be normal if the group G R 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.
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