（G, s）-Transitive Graphs of Valency 7  

作　　者：Songtao Guo Yantao Li Xiaohui Hua 

机构地区：[1]School of Mathematics and Statistics, Henan University of Science and Technology Luoyang, Henan 471023, China [2]College of Arts and Science, Beijing Union University, Beijing 100091, China [3]College of Mathematics and Information Science, Henan Normal University Xinxiang, Henan 453007, China

出　　处：《Algebra Colloquium》2016年第3期493-500,共8页代数集刊（英文版）

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）.

摘　　要：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.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.

关 键 词：symmetric graph s-transitive graph （G s）-transitive graph 

分 类 号：O157.5[理学—数学] O152.1[理学—基础数学]