Geodesic
On normal 2-geodesic transitive Cayley graphs
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 4, pp. 903-918.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We investigate connected normal 2-geodesic transitive Cayley graphs $\mathrm{Cay}(T,S)$. We first prove that if $\mathrm{Cay}(T,S)$ is neither cyclic nor $K_{4\vert 2\vert}$, then $\langle a\rangle\backslash\{1\}\subsetneq S$ for all $a \in S$. 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.
Classification : 05C25
Keywords: Cayley graph, normal 2-geodesic transitivity 
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     title = {On normal 2-geodesic transitive {Cayley} graphs},
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Devillers, Alice; Jin, Wei; Li, Cai Heng; Praeger, Cheryl E. On normal 2-geodesic transitive Cayley graphs. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 4, pp. 903-918. http://geodesic.mathdoc.fr/item/JAC_2014__39_4_a3/