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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (1): 60-66    DOI: 10.3785/j.issn.1008-9497.2020.01.008
数学与计算机科学     
完全二部图K 10, n (215 ≤ n ≤ 466)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, 宁夏银川 750021
Vertex-distinguishing E-total coloring of complete bipartite graph K 10, n with 215 ≤ n ≤ 466.
BAO Liya1, CHEN Xiangen1, WANG Zhiwen2
1.College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.College of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
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摘要： 图G的一个E-全染色是指使相邻点染以不同的颜色，且每条关联边和它的端点染以不同的颜色的全染色。对图G的一个E-全染色f, 一旦对图G中任意互不相同的两点 u, v ，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，那么f称为图G的点可区别的E-全染色，简称为VDET染色。令χvt e(G)=min{k|G存在k-VDET染色，称χvt e(G)为图G的点可区别E-全色数。运用分析法和反证法，讨论并证明了完全二部图K 10, n (215 ≤ n ≤ 466)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. A total coloring f of G is called an E-total coloring if any two adjacent vertices of G receive different colors, and any edge of G receives the color different from those of its endpoints. Let C(x) denote the set of colors of vertex x and of the edges incident with x under f for an E-total coloring f of a graph G, if C(u)≠ C(v) for any two distint vertice u and v of V（G）,then f is called a vertex-distinguishing E-total coloring of G. Let χvt e(G)=min{k G has a k-VDET coloring}, Then χvt e(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10n is investigated and the VDET chromatic number of K 10, n (215 ≤ n ≤ 466) has been obtained.
Key words: complete bipartite graphs    E-total coloring    vertex-distinguishing E-total coloring    vertex-distinguishing E-total chromatic number
收稿日期: 2018-07-31 出版日期: 2020-01-25
CLC:  O157.5  
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（2018AAC03055);宁夏百人计划项目.
通讯作者: ORCID:http://orcid.org/0000-0002-2243-3718，E-mail: chenxe@nwnu.edu.cn.     E-mail: baoliya20170820bly@163.com.
作者简介: 包丽娅(1993―)，ORCID:http://orcid.org/0000-0001-5155-3893，女，硕士研究生，主要从事图论及其应用研究，E-mail:baoliya20170820bly@163.com.
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引用本文:

包丽娅, 陈祥恩, 王治文. 完全二部图K 10, n (215 ≤ n ≤ 466)的点可区别E-全染色[J]. 浙江大学学报（理学版）, 2020, 47(1): 60-66.

BAO Liya, CHEN Xiangen, WANG Zhiwen. Vertex-distinguishing E-total coloring of complete bipartite graph K 10, n with 215 ≤ n ≤ 466.. Journal of Zhejiang University (Science Edition), 2020, 47(1): 60-66.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.01.008    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I1/60

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