(G, s)-Transitive Graphs Of Valency 15
Abstract
Let $X$ be a finite simple undirected graph and $G\leq \rm{Aut}(X)$. If $G$ is transitive on the set of $s$-arcs but not on the set of $(s+1)$-arcs of $X$, then $X$ is called $(G, s)$-transitive. In this paper, we determine the structure of the vertex-stabilizer $G_{v}$ when $X$ is a connected $(G,s)$-transitive graph of valency $15$. We also give some examples to show that each type of $G_{v}$ with $s\ge 2$, can be realized.
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