Geodesic
Hexavalent $(G,s)$-transitive graphs
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 923-931.

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Let $X$ be a finite simple undirected graph with a subgroup $G$ of the full automorphism group ${\rm Aut}(X)$. Then $X$ is said to be $(G,s)$-transitive for a positive integer $s$, if $G$ is transitive on $s$-arcs but not on $(s+1)$-arcs, and $s$-transitive if it is $({\rm Aut}(X),s)$-transitive. Let $G_v$ be a stabilizer of a vertex $v\in V(X)$ in $G$. Up to now, the structures of vertex stabilizers $G_v$ of cubic, tetravalent or pentavalent $(G,s)$-transitive graphs are known. Thus, in this paper, we give the structure of the vertex stabilizers $G_v$ of connected hexavalent $(G,s)$-transitive graphs.
DOI : 10.1007/s10587-013-0062-9
Classification : 05C25, 20B25
Keywords: symmetric graph; $s$-transitive graph; $(G, s)$-transitive graph 
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Guo, Song-Tao; Hua, Xiao-Hui; Li, Yan-Tao. Hexavalent $(G,s)$-transitive graphs. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 923-931. doi : 10.1007/s10587-013-0062-9. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0062-9/

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