Halin图的2-距离和可区别全染色  

2-Distance sum distinguishing total coloring of Halin graphs

作　　者：王同昕 杨超 殷志祥 姚兵 WANG Tongxin;YANG Chao;YIN Zhixiang;YAO Bing(School of Mathematics,Physics and Statistics,Center of Intelligent Computing and Applied Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]上海工程技术大学数理与统计学院/智能计算与应用统计研究中心,上海201620 [2]西北师范大学数学与统计学院,兰州730070

出　　处：《华中师范大学学报（自然科学版）》2024年第5期507-510,525,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(61672001,61662066,62072296).

摘　　要：记[k]={1,2,…,k}为颜色集.设f:V(G)∪E(G)→[k]为图G的一个k-全染色.令S(u)=f(u)+∑/_(v)∈N_(G)(u)f(uv),其中,N_(G)(u)表示u的邻点集.若对G中距离不超过2的任意两点u、v,有S(u)≠S(v),则称f为图G的一个2-距离和可区别k-全染色.图G的2-距离和可区别k-全染色中最小k值称为图G的2-距离和可区别全色数,记为χ″_(2-Σ)(G).该文运用组合零点定理证明了最大度至少为4的Halin图G满足χ″_(2-Σ)(G)≤max{Δ(G)+2,9},其中,Δ(G)表示图G的最大度.Let[k]={1,2,…,k}be a color set.Let f:V(G)∪E(G)→[k]be a k-total coloring of G.Set S(u)=f(u)+∑/_(v)∈N_(G)(u)f(uv),where N_(G)(u)is the neighbor set of vertex u.If S(u)≠S(v)for any two vertices u,v with their distance is not more than 2,then f is called the 2-distance sum distinguishing k-total coloring of G.The smallest value k that G admits a 2-distance sum distinguishing k-total coloring of G is called the 2-distance sum distinguishing total chromatic number of G,and denoted byχ″_(2-Σ)(G).By using Combinatorial Nullstellensatz,it is proved thatχ″_(2-Σ)(G)≤max{Δ(G)+2,9}for Halin graph G with maximum degreeΔ(G)≥4.

关 键 词：2-距离和可区别全染色 HALIN图 组合零点定理 

分 类 号：O157.5[理学—数学]