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Guo, Song-Tao; Feng, Yan-Quan
Discrete mathematics, 08/2012, Letnik: 312, Številka: 15Journal Article
A graph, with a group G of its automorphisms, is said to be (G,s)-transitive if G is transitive on s-arcs but not on (s+1)-arcs of the graph. Let X be a connected (G,s)-transitive graph for some s≥1, and let Gv be the stabilizer of a vertex v∈V(X) in G. In this paper, we determine the structure of Gv when X has valency 5 and Gv is non-solvable. Together with the results of Zhou and Feng J.-X. Zhou, Y.-Q. Feng, On symmetric graphs of valency five, Discrete Math. 310 (2010) 1725–1732, the structure of Gv is completely determined when X has valency 5. For valency 3 or 4, the structure of Gv is known.
