Hexavalent (G,s)-transitive graphs |
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Authors: | Song-Tao Guo Xiao-Hui Hua Yan-Tao Li |
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Institution: | 1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, P.R. China 2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China 3. College of Arts and Science, Beijing Union University, Beijing, 100091, P.R. China
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Abstract: | Let X be a finite simple undirected graph with a subgroup G of the full automorphism group 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 (Aut(X), s)-transitive. Let G v be a stabilizer of a vertex v ∈ 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. |
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