三星的最优的一般点可区别全染色

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英文篇名：Optimal General Vertex-Distinguishing Total Colorings of Tristars 作者：李婷 ; 陈祥恩 ; 王治文 英文作者：LI Ting;CHEN Xiang'en;WANG Zhiwen;College of Mathematics and Statistics, Northwest Normal University;School of Mathematics and Computer Sciences, Ningxia University; 关键词：三星 ; 一般全染色 ; 一般点可区别全染色 ; 一般点可区别全色数 英文关键词：tristar;;general total coloring;;general vertex-distinguishing total coloring;;general vertex-distinguishing total chromatic number 中文刊名：STDX 英文刊名：Journal of Shantou University(Natural Science Edition) 机构：西北师范大学数学与统计学院;宁夏大学数学计算机科学学院; 出版日期：2018-08-15 出版单位：汕头大学学报(自然科学版) 年：2018 期：v.33;No.98 基金：国家自然科学基金资助项目(11761064,61163037,11261046);; 宁夏回族自治区百人计划资助项目 语种：中文; 页：STDX201803003 页数：6 CN：03 ISSN：44-1059/N 分类号：20-25

摘要

设G为简单图.所谓G的k-一般全染色f是指从V(G)∪E(G)到{1,2,…,k}的一个映射.设f为G的一个一般全染色,x为G的一个顶点,令C(x)={f(xu)xu∈E}∪{f(x)},称之为顶点x在f下的色集合.设f是G的一个一般全染色,若对图G的任意两个不同的顶点u,v,有C(u)≠C(v),则f称为图G的一般点可区别全染色(GVDTC).本文给出了三星的最优的一般点可区别全染色.
        Let G be a simple graph. A general total k-coloring of G is a mapping f :V(G)∪E(G)→{1, 2…, k}. Let f be a general total coloring of G and x be a vertex of G, C(x)={f(xu) xu∈E}∪{f(x)}, which is called the color set of vertex x under f. For a general total coloring f of G, if C(u)≠C(v) for any two different vertices u and v of G, then f is called a general vertexdistinguishing total coloring of G(or GVDTC of G for short). The optimal general vertexdistinguishing total colorings of tristars are given.

引文

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