完全二部图K3,n(3≤n≤17)的点可区别E-全染色

吉林大学学报(理学版)

完全二部图K_3,n(3≤n≤17)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, 兰州 730070; 2. 宁夏大学数学与计算机科学学院, 银川 750021

收稿日期:2015-03-24 出版日期:2015-11-26 发布日期:2015-11-23
通讯作者: 李世玲 E-mail:lishilingjjwai@163.com

VertexDistinguishing E-Total Coloring of CompleteBipartite Graph K_3,n with 3≤n≤17

LI Shiling¹, CHEN Xiang’en¹, WANG Zhiwen²

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

Received:2015-03-24 Online:2015-11-26 Published:2015-11-23
Contact: LI Shiling E-mail:lishilingjjwai@163.com

摘要/Abstract

摘要：

设G是一个简单图, 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关联边颜色所构成的集合. 若u,v∈V(G), u≠v, 有C(u)≠C(v), 则f称为图G的点可区别E-全染色, 简称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(简称为VDET色数), 记为χ^e_vt(G). 利用分析法和反证法, 讨论并给出完全二部图K_3,n(3≤n≤17)的点可区别E全色数.

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

Abstract:

Let G be a simple graph, f is a total coloring of G. 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 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 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. Based on the analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K_3,n was discussed and the VDET chromatic number of K_3,n(3≤n≤17) was obtained.

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

中图分类号:

O157.5

李世玲, 陈祥恩, 王治文. 完全二部图K_3,n(3≤n≤17)的点可区别E-全染色[J]. 吉林大学学报(理学版), 2015, 53(06): 1171-1176.

LI Shiling, CHEN Xiang’en, WANG Zhiwen. VertexDistinguishing E-Total Coloring of CompleteBipartite Graph K_3,n with 3≤n≤17[J]. Journal of Jilin University Science Edition, 2015, 53(06): 1171-1176.

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