Abstract
We investigate connected normal 2-geodesic transitive Cayley graphs Cay(T,S). We first prove that if Cay(T,S) is neither cyclic nor K4[2], then ?a??{1}⊆?S for all a?S. Next, as an application, we give a reduction theorem proving that each graph in this family which is neither a complete multipartite graph nor a bipartite 2-arc transitive graph, has a normal quotient that is either a complete graph or a Cayley graph in the family for a characteristically simple group. Finally we classify complete multipartite graphs in the family.
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