一类含有4-圈的单圈图一般点可区别全染色

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英文篇名：General vertex-distinguishing total colorings of a family of unicyclic graphs including C_4 作者：陈祥恩 ; 李婷 ; 王治文 英文作者：CHEN Xiang′en;LI Ting;WANG Zhiwen;College of Mathematics and Statistics,Northwest Normal University;School of Mathematics and Computer Sciences,Ningxia University; 关键词：单圈图 ; 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：unicyclic graphs;;general total coloring;;general vertex-distinguishing total coloring;;general vertex-distinguishing total chromatic number 中文刊名：DLLG 英文刊名：Journal of Dalian University of Technology 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：2017-05-25 14:48 出版单位：大连理工大学学报 年：2017 期：v.57 基金：国家自然科学基金资助项目(61163037,61163054,11261046);; 宁夏回族自治区百人计划资助项目 语种：中文; 页：DLLG201703015 页数：5 CN：03 ISSN：21-1117/N 分类号：99-103

摘要

设G为简单图.设f是图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),则称f为图G的一般点可区别全染色(简记为GVDTC).对图G进行一般点可区别全染色所需要的最少颜色数称为图G的一般点可区别全色数.将一类含有4-圈的单圈图悬挂边的染色按从小到大的顺序排列,探讨了它的一般点可区别全染色,确定了它具有一般点可区别全染色,并得到了它的一般点可区别全色数.
        Let Gbe a simple graph.For a general total coloring fof G,if C(u)≠C(v)for any two different vertices uand v of G,then fis called a general vertex-distinguishing total coloring of G(or GVDTC of Gfor short).The minimum number of colors required in a GVDTC is the general vertexdistinguishing total chromatic number.The general vertex-distinguishing total colorings of a family of unicyclic graphs including C4 are discussed by making the coloring of its pendent edges in an ascending order.It is determined that it has a general vertex-distinguishing total coloring of Gand its general vertex-distinguishing total chromatic number is got.

引文

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