完全二部图K10,n(10≤n≤90)的点可区别E-全染色

doi:10.6040/j.issn.1671-9352.0.2018.605

《山东大学学报(理学版)》 ›› 2018, Vol. 53 ›› Issue (12): 23-30.doi: 10.6040/j.issn.1671-9352.0.2018.605

完全二部图K10,n(10≤n≤90)的点可区别E-全染色

包丽娅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.宁夏大学数学统计学院, 宁厦银川 750021

出版日期:2018-12-20 发布日期:2018-12-18
作者简介:包丽娅(1993— ),女,硕士研究生,研究方向为图论及其应用. E-mail:baoliya20170820bly@163.com
基金资助:
国家自然科学基金资助项目(11761064,61163037,11261046);宁夏自然科学基金资助项目(2018AAC03005);宁夏回族自治区百人计划资助项目

Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90

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

Online:2018-12-20 Published:2018-12-18

摘要/Abstract

摘要： 图G的一个E-全染色f是指使相邻点染以不同颜色且每条关联边与它的端点染以不同颜色的全染色。对图G的一个E-全染色f,一旦∠u,v∈V(G), u≠v,就有C(u)≠C(v),其中C(x)表示在f下点x的颜色以及与x关联的边的色所构成的集合,则f称为图G的点可区别的E-全染色,简称为VDET染色。令χ^e_vt(G)=min{k|G存在k-VDET染色},称χ^e_vt(G)为图G的点可区别E-全色数。利用分析法和反证法,讨论并给出了完全二部图K_10,n(10≤n≤90)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. An E-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, and no edges of G receives the same color as one of its endpoints. For an E-total coloring f of G, if C(u)≠C(v) for any two distinct vertices u and v of V(G), where C(x) denotes the set of colors of vertex x and of the edges incident with x under f, then f is called a vertex-distinguishing E-total coloring of G. Let χ^e_vt(G)=min{k|G has a k-VDET coloring}. Then χ^e_vt(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10,n is discussed and the VDET chromatic number of K10,n(10≤n≤90) has been 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

包丽娅,陈祥恩,王治文. 完全二部图K10,n(10≤n≤90)的点可区别E-全染色[J]. 《山东大学学报(理学版)》, 2018, 53(12): 23-30.

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完全二部图K10,n(10≤n≤90)的点可区别E-全染色

Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90

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