The Adjacent Vertex Distinguishing Total Chromatic Number of Some Families of Snarks

被引：0
|
作者：
Chen, Qin [1 ]
机构：
[1] China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China
来源：
ARS COMBINATORIA | 2017年 / 132卷
关键词：
Adjacent vertex distinguishing total coloring; Loupekhine snark; Blanusa snark; GRAPHS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The adjacent vertex distinguishing total chromatic number chi(at)(G) of a graph G is the smallest integer kappa for which G admits a proper k total coloring such that no pair of adjacent vertices are incident to the same set of colors.Snarks are connected bridgeless cubic graphs with chromatic index 4.In this paper, we show that chi(at)(G) = 5 for two infinite subfamilies of snarks, i.e., the Loupekhine snark and Blanusa snark of first and second kind.In addition, we give an adjacent vertex distinguishing total coloring using 5 colors for Watkins snark and Szekeres snark, respectively.
引用
收藏
页码：311 / 321
页数：11
相关论文
共 50 条
  • [1] The adjacent vertex distinguishing total chromatic number
    Coker, Tom
    Johannson, Karen
    [J]. DISCRETE MATHEMATICS, 2012, 312 (17) : 2741 - 2750
  • [2] On the Adjacent Vertex Strong Distinguishing Total chromatic number of Some Graphs
    Yan, Qiantai.
    Li, Wuzhuang.
    [J]. 2013 INTERNATIONAL CONFERENCE ON INFORMATION TECHNOLOGY AND APPLICATIONS (ITA), 2013, : 391 - 394
  • [3] The Adjacent Vertex Distinguishing Total Chromatic Number of Graphs
    Wang, Zhiwen
    Zhu, Enqiang
    [J]. 2010 4TH INTERNATIONAL CONFERENCE ON BIOINFORMATICS AND BIOMEDICAL ENGINEERING (ICBBE 2010), 2010,
  • [4] The total-chromatic number of some families of snarks
    Campos, C. N.
    Dantas, S.
    de Mello, C. P.
    [J]. DISCRETE MATHEMATICS, 2011, 311 (12) : 984 - 988
  • [5] A Note on the Adjacent Vertex Distinguishing Total Chromatic Number of Some Cubic Graphs
    Chen, Qin
    [J]. ARS COMBINATORIA, 2016, 124 : 319 - 327
  • [6] A note on the adjacent vertex distinguishing total chromatic number of graph
    Wang, Zhiwen
    [J]. ADVANCED MATERIALS AND COMPUTER SCIENCE, PTS 1-3, 2011, 474-476 : 2341 - 2345
  • [7] A note on the adjacent vertex distinguishing total chromatic number of graphs
    Huang, Danjun
    Wang, Weifan
    Yan, Chengchao
    [J]. DISCRETE MATHEMATICS, 2012, 312 (24) : 3544 - 3546
  • [8] On the adjacent vertex distinguishing total chromatic number of outer plane graph
    Wang, Zhi-wen
    Yan, Li-hong
    Lee, Jaeun
    Zhang, Zhong-fu
    [J]. ARS COMBINATORIA, 2012, 107 : 499 - 514
  • [9] Upper bounds on adjacent vertex distinguishing total chromatic number of graphs
    Hu, Xiaolan
    Zhang, Yunqing
    Miao, Zhengke
    [J]. DISCRETE APPLIED MATHEMATICS, 2017, 233 : 29 - 32
  • [10] On Adjacent Vertex-Distinguishing Total Chromatic Number of Generalized Petersen Graphs
    Zhu, Enqiang
    Jiang, Fei
    Li, Zepeng
    Shao, Zehui
    Xu, Jin
    [J]. 2016 IEEE FIRST INTERNATIONAL CONFERENCE ON DATA SCIENCE IN CYBERSPACE (DSC 2016), 2016, : 230 - 234
12345