文献类型：期刊文献

英文题名：Pentavalent symmetric graphs of order twice a prime power

作者：Feng, Yan-Quan[1];Zhou, Jin-Xin[1];Li, Yan-Tao[2]

第一作者：Feng, Yan-Quan

通讯作者：Feng, YQ[1]

机构：[1]Beijing Jiaotong Univ, Math, Beijing 100044, Peoples R China;[2]Beijing Union Univ, Coll Arts & Sci, Beijing 100191, Peoples R China

第一机构：Beijing Jiaotong Univ, Math, Beijing 100044, Peoples R China

通讯机构：[1]corresponding author), Beijing Jiaotong Univ, Math, Beijing 100044, Peoples R China.

年份：2016

卷号：339

期号：11

起止页码：2640-2651

外文期刊名：DISCRETE MATHEMATICS

收录：;Scopus(收录号：2-s2.0-84973300510);WOS:【SCI-EXPANDED(收录号:WOS:000380593200006)】；

基金：This work was supported by the National Natural Science Foundation of China (11571035, 11231008, 11271012) and by the 111 Project of China (B16002).

语种：英文

外文关键词：Symmetric graph; Cayley graph; Regular covering; Normal cover

摘要：A connected symmetric graph of prime valency is basic if its automorphism group contains no nontrivial normal subgroup having more than two orbits. Let p be a prime and n a positive integer. In this paper, we investigate properties of connected pentavalent symmetric graphs of order 2p(n), and it is shown that a connected pentavalent symmetric graph of order 2p(n) is basic if and only if it is either a graph of order 6, 16, 250, or a graph of three infinite families of Cayley graphs on generalized dihedral groups-one family has order 2p with p = 5 or 5 vertical bar (p - 1), one family has order 2p(2) with 5 vertical bar (p +/- 1), and the other family has order 2p(4). Furthermore, the automorphism groups of these basic graphs are computed. Similar works on cubic and tetravalent symmetric graphs of order 2p(n) have been done. It is shown that basic graphs of connected pentavalent symmetric graphs of order 2p(n) are symmetric elementary abelian covers of the dipole Dip(5), and with covering techniques, uniqueness and automorphism groups of these basic graphs are determined. Moreover, symmetric Z(p)(n)-covers of the dipole Dip(5) are classified. As a byproduct, connected pentavalent symmetric graphs of order 2p(2) are classified. (C) 2016 Elsevier B.V. All rights reserved.