Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph ...Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.展开更多
基金This work was supported by the National Natural Science Foundation of China （11301154, 11271012, 11301159, 11101035, 11326056）, the Key Project of Education Department of Henan Province Scientific and Technological Research （13A110249） and the Scientific Re- search Foundation for Doctoral Scholars of HAUST （09001707）.
文摘Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.
