Let X be a connected G-locally primitive arc-transitive graph for some sub-group G of Aut(X).Suppose that X is a(G,s)-transitive graph.In this paper,we give a characterization of the vertex-stabilizer G,when X has val...Let X be a connected G-locally primitive arc-transitive graph for some sub-group G of Aut(X).Suppose that X is a(G,s)-transitive graph.In this paper,we give a characterization of the vertex-stabilizer G,when X has valency 8.展开更多
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
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It fo...A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.展开更多
A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. We classify connected heptavalent symmetric graphs of order 16p for each prime p. As a result, there are two such spora...A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. We classify connected heptavalent symmetric graphs of order 16p for each prime p. As a result, there are two such sporadic graphs with p=3 and 7, and an infinite family of 1-regular normal Cayley graphs on the group Z23 × D2p with 7｜（p - 1）.展开更多
文摘Let X be a connected G-locally primitive arc-transitive graph for some sub-group G of Aut(X).Suppose that X is a(G,s)-transitive graph.In this paper,we give a characterization of the vertex-stabilizer G,when X has valency 8.
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.
基金Supported by the National Natural Science Foundation of China(No.11301154,11301151,11201401,11271012)the Key Project of Education Department of Henan Province Scientific and Technological Research(No.13A110249)the Scientific Research Foundation for Doctoral Scholars of HAUST(No.09001707)
文摘A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.
文摘A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. We classify connected heptavalent symmetric graphs of order 16p for each prime p. As a result, there are two such sporadic graphs with p=3 and 7, and an infinite family of 1-regular normal Cayley graphs on the group Z23 × D2p with 7｜（p - 1）.
