Vertex Distinguishing Edge- and Total-Colorings of Cartesian and other Product Graphs

被引：0
作者：
Baril, Jean-Luc [1 ]
Kheddouci, Hamamache [2 ]
Togni, Olivier [1 ]
机构：
[1] Univ Bourgogne, CNRS, UMR 5158, LE2I, F-21078 Dijon, France
[2] Univ Lyon 1, LIESP, F-69622 Villeurbanne, France
来源：
ARS COMBINATORIA | 2012年 / 107卷
关键词：
graph; edge-coloring; vertex-distinguishing; adjacent vertex-distinguishing; total coloring; total adjacent vertex-distinguishing; graph products;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies edge- and total-colorings of graphs in which (all or only adjacent) vertices are distinguished by their sets of colors. We provide bounds for the minimum number of colors needed for such colorings for the Cartesian product of graphs along with exact results for generalized hypercubes. We also present general bounds for the direct, strong and lexicographic products.
引用
收藏
页码：109 / 127
页数：19
相关论文
共 50 条
  • [1] ADJACENT VERTEX DISTINGUISHING EDGE-COLORINGS AND TOTAL-COLORINGS OF THE CARTESIAN PRODUCT OF GRAPHS
    Tian, Shuangliang
    Chen, Ping
    Shao, Yabin
    Wang, Qian
    NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2014, 4 (01): : 49 - 58
  • [2] Adjacent vertex distinguishing edge-colorings and total-colorings of the lexicographic product of graphs
    Tian, Shuangliang
    Wang, Qian
    DISCRETE APPLIED MATHEMATICS, 2015, 185 : 220 - 226
  • [3] Vertex-distinguishing edge colorings of graphs
    Ballister, PN
    Riordan, OM
    Schelp, RH
    JOURNAL OF GRAPH THEORY, 2003, 42 (02) : 95 - 109
  • [4] Gap vertex-distinguishing edge colorings of graphs
    Tahraoui, M. A.
    Duchene, E.
    Kheddouci, H.
    DISCRETE MATHEMATICS, 2012, 312 (20) : 3011 - 3025
  • [5] Adjacent vertex distinguishing total colorings of graphs with four distinguishing constraints
    Yang, Chao
    Ren, Han
    Yao, Bing
    ARS COMBINATORIA, 2016, 127 : 197 - 208
  • [6] Union vertex-distinguishing edge colorings
    Kittipassorn, Teeradej
    Sanyatit, Preechaya
    DISCRETE MATHEMATICS, 2024, 347 (09)
  • [7] Vertex-Distinguishing Edge Colorings of Graphs with Degree Sum Conditions
    Bin Liu
    Guizhen Liu
    Graphs and Combinatorics, 2010, 26 : 781 - 791
  • [8] Vertex-Distinguishing Edge Colorings of Graphs with Degree Sum Conditions
    Liu, Bin
    Liu, Guizhen
    GRAPHS AND COMBINATORICS, 2010, 26 (06) : 781 - 791
  • [9] Distinguishing colorings of Cartesian products of complete graphs
    Fisher, Michael J.
    Isaak, Garth
    DISCRETE MATHEMATICS, 2008, 308 (11) : 2240 - 2246
  • [10] On Vertex-Distinguishing Proper Edge Colorings of Graphs Satisfying the Ore Condition
    Chen, Meirun
    Guo, Xiaofeng
    ARS COMBINATORIA, 2010, 97 : 377 - 382
12345