完全二部图K3,n(n≥18)的点可区别E-全染色

doi:10.6040/j.issn.1671-9352.0.2015.059

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 68-71.doi: 10.6040/j.issn.1671-9352.0.2015.059

完全二部图K3,n(n≥18)的点可区别E-全染色

李世玲¹, 陈祥恩¹,王治文²

1.西北师范大学数学与统计学院, 甘肃兰州 730070;2.宁夏大学数学与计算机科学学院, 宁夏银川 750021

收稿日期:2015-01-30 出版日期:2016-04-20 发布日期:2016-04-08
作者简介:李世玲(1991— ), 女, 硕士研究生, 主要研究方向为图论及其应用. E-mail:lishilingjjwai@163.com
基金资助:
国家自然科学基金资助项目(61163037,61163054,11261046,61363060);宁夏百人计划资助项目(Theprojectofone-hundredscholarsplanofNingxia)

Vertex-Distinguishing E-Total coloring of complete bipartite graph K3,n with n≥18

LI Shi-ling¹, CHEN Xiang-en¹, WANG Zhi-wen²

1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
2. School of Mathematics and Computer Sciences, Ningxia University, Yinchuan 750021, Ningxia, China

Received:2015-01-30 Online:2016-04-20 Published:2016-04-08

摘要/Abstract

摘要： G是一个简单图, G 的一个E-全染色f是指使相邻点着不同色且每条关联边与它的端点着以不同的色的全染色。设 f 为 G 的一个E-全染色。对任意点x∈V(G), 用C(x)表示在 f 下点 x 的色以及与 x 关联的边的颜色所构成的集合。若 ∠u,v∈V(G),u≠v, 有C(u)≠C(v), 则 f 称为是图G的点可区别的E-全染色, 简称为VDET染色。图G的VDET染色所用颜色数目的最小值称为图 G 的点可区别E-全色数或简称为 VDET 色数, 记为χ^e_vt(G)。讨论并给出了完全二部图K_3,n(n≥18)的点可区别E-全色数。

关键词: 点可区别E-全染色, E-全染色, 点可区别E-全色数, 完全二部图

Abstract: Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x)denote the set of colors of vertex x and of the edges incident with x, we call C(x)the color set of x. If C(u)≠C(v)for any two different vertices u and v of V(G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short。 The minimum number of colors required for a VDET coloring of G is denoted by χ^e_vt(G)and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K3,n is discussed in paper and the VDET chromatic number of K3,n(n≥18)has been obtained.

Key words: complete bipartite graphs, vertex-distinguishing E-total chromatic number, vertex-distinguishing E-total coloring, E-total coloring

中图分类号:

O157.5

李世玲, 陈祥恩,王治文. 完全二部图K3,n(n≥18)的点可区别E-全染色[J]. 山东大学学报（理学版）, 2016, 51(4): 68-71.

LI Shi-ling, CHEN Xiang-en, WANG Zhi-wen. Vertex-Distinguishing E-Total coloring of complete bipartite graph K3,n with n≥18[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 68-71.

参考文献

[1] ZHANG Zhongfu, QIU Pengxiang, LI Jingwen, et al. Vertex distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.
[2] CHEN Xiangen. Asymptotic behavior of the vertex-distinguishing total chromatic numbers of n-cubes[J]. Journal of Northwest Normal University Natural Science Edition, 2005, 41(5):1-3.
[3] CHEN Xiangen, GAO Yuping, YAO Bing. Relations of vertex distinguishing total chromatic numbers between a subgraph and its supergraph[J]. Information Sciences, 2014, 288:246-253.
[4] 辛小青, 陈祥恩. m 个点不交的 C4 的并的点可区别全染色[J]. 山东大学学报(理学版), 2010, 45(10):35-39. XIN Xiaoqing, CHEN Xiangen. Vertex distinguishing total chromatic number of mC4[J]. Journal of Shandong University(Science Edition), 2012, 45(10):35-39.
[5] 陈祥恩, 王治文, 马彦荣, 等. mK4的点可区别全染色[J]. 吉林大学学报(理学版), 2012, 50(4):686-692. CHEN Xiangen, WANG Zhiwen, MA Yanrong, et al. Vertex-distinguishing total colorings of mK4[J]. Journal of Jilin University(Science Edition), 2012, 50(4):686-692.
[6] CHEN Xiangen, ZU Yue, ZHANG Zhongfu. Vertex-distinguishing E-total colorings of graphs[J]. Arab J Sci Eng, 2011, 36:1485-1500.
[7] CHEN Xiangen, ZU Yue. Vertex-distinguishing E-total coloring of the graphs mC3 and mC4[J]. Journal of Mathematical Research & Exposition, 2011, 31:45-58.
[8] BONDY J A, MURTY U S R. Graph theory[M]. London: Springer, 2008.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

完全二部图K3,n(n≥18)的点可区别E-全染色

Vertex-Distinguishing E-Total coloring of complete bipartite graph K3,n with n≥18

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

多维度评价

本文评价

推荐阅读 0

[1]	寇艳芳,陈祥恩,王治文. K1,3,p和 K1,4,p的点可区别的IE-全染色及一般全染色[J]. 山东大学学报（理学版）, 2018, 53(8): 53-60.
[2]	刘信生, 邓卫东, 王志强. 直积图邻点可区别E-全染色的一些结论[J]. 山东大学学报（理学版）, 2015, 50(02): 5-8.
[3]	李振琳,卢君龙,吕新忠. 关于图的符号边全控制[J]. J4, 2012, 47(6): 83-86.
[4]	王国兴. 点不交的m个C₃的并的点可区别IE-全染色[J]. J4, 2011, 46(2): 57-61.
[5]	何文玉，陈祥恩*. 完全二部图K5,n的点可区别IE全染色[J]. J4, 2009, 44(2): 91-96.