Edge-Transitive Regular Metacyclic Covers of the Petersen Graph

被引：5
|
作者：
Pan, Jiangmin [1 ,2 ]
Huang, Zhaohong [2 ]
机构：
[1] Yunnan Univ Finance & Econ, Sch Math & Stat, Kunming, Peoples R China
[2] Yunnan Univ, Sch Math & Stat, Kunming, Peoples R China
来源：
GRAPHS AND COMBINATORICS | 2016年 / 32卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Regular cover; Metacyclic group; Normal quotient graph; ELEMENTARY ABELIAN COVERS; CUBIC SYMMETRIC GRAPHS;
D O I：
10.1007/s00373-015-1597-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a complete classification is given of all the regular metacyclic covers of the Petersen graph, whose fibre-preserving groups act edge-transitively. Moreover, as an application, it is proved that there is no cubic 1-arc-regular graph with order 5m where m is a cube-free integer and coprime to 15.
引用
收藏
页码：777 / 784
页数：8
相关论文
共 50 条
  • [41] DOUBLE CYCLE COVERS AND THE PETERSEN GRAPH
    CATLIN, PA
    JOURNAL OF GRAPH THEORY, 1989, 13 (04) : 465 - 483
  • [42] ON GRAPHS WITH EDGE-TRANSITIVE AUTOMORPHISM-GROUPS
    STELLMACHER, B
    ILLINOIS JOURNAL OF MATHEMATICS, 1984, 28 (02) : 211 - 266
  • [43] A Classification of Orientably Edge-Transitive Circular Embeddings of
    Fan, Wenwen
    Li, Cai Heng
    Qu, Hai Peng
    ANNALS OF COMBINATORICS, 2018, 22 (01) : 135 - 146
  • [44] Finite primitive groups and edge-transitive hypergraphs
    Pablo Spiga
    Journal of Algebraic Combinatorics, 2016, 43 : 715 - 734
  • [45] On edge-transitive Cayley graphs of valency four
    Fang, XG
    Li, CH
    Xu, MY
    EUROPEAN JOURNAL OF COMBINATORICS, 2004, 25 (07) : 1107 - 1116
  • [46] Finite normal edge-transitive Cayley graphs
    Praeger, CE
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1999, 60 (02) : 207 - 220
  • [47] On Reconstruction of Normal Edge-Transitive Cayley Graphs
    Khosravi, Behnam
    Khosravi, Behrooz
    Khosravi, Bahman
    ANNALS OF COMBINATORICS, 2020, 24 (04) : 791 - 807
  • [48] Classifying a family of edge-transitive metacirculant graphs
    Song, Shu-Jiao
    Li, Cai Heng
    Wang, Dianjun
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2012, 35 (03) : 497 - 513
  • [49] Finite edge-transitive bi-circulants
    Pan, Jiangmin
    Yin, Fugang
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 405
  • [50] 2-Arc-transitive metacyclic covers of complete graphs
    Xu, Wenqin
    Du, Shaofei
    Kwak, Jin Ho
    Xu, Mingyao
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2015, 111 : 54 - 74
12345