两类笛卡尔乘积图的邻点全和可区别全染色  

Neighbor full sum distinguishing total coloring of two types of Cartesian product graphs

作　　者：叶宏波 杨超 殷志祥 姚兵[3] YE Hongbo;YANG Chao;YIN Zhixiang;YAO Bing(School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;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,上海201620 [2]上海工程技术大学智能计算与应用统计研究中心,上海201620 [3]西北师范大学数理与统计学院,兰州730070

出　　处：《上海工程技术大学学报》2022年第1期91-97,共7页Journal of Shanghai University of Engineering Science

基　　金：国家自然科学基金资助(61672001,61662066,62072296)。

摘　　要：设f:V(G)∪E(G)→{1,2,…k}是图G的一个正常k−全染色,令权重■,其中N(x)={y∈V(G)∣xy∈E(G)}.对任意的边vu∈E(G),如果ψ(u)≠ψ(v)有成立,则称f为图的一个邻点全和可别正常k正常k−全染色.图G的邻点全和可区别全色数是指对图进行邻点全和可区别k−全染色所需要的最小色数k,记为ftndi∑(G).本研究猜想:对于最大度为∆的图G(除K_(2)外),ftndi∑(G)≤∆+2.研究得到路与路的笛卡尔乘积图和路与圈的笛卡尔乘积图的邻点全和可区别全色数均为∆+1,证实了上述猜想.Let f:V(G)∪E(G)→{1,2,…k}be a proper k-total coloring of a graph G.Define a weight function on total coloring as■,where N(x)={y∈V(G)∣xy∈E(G)}.If ψ(u)≠ψ(v) for vu∈E(G)any edge,then f is called a neighbor full sum distinguishing k-total coloring of G.The smallest value k for which G admins a neighbor full sum distinguishing total coloring with k colors is called the neighbor full sum distinguishing total chromatic number of G and denoted by ftndi∑(G).The research conjectures that ftndi∑(G)≤∆+2 for every graph except for K_(2),whereΔrepresents the maximum degree of G.Meanwhile,we get this parameter for Cartesian product graphs of paths and paths,paths and cycles areΔ+1,respectively,which confirm the above conjecture.

关 键 词：正常全染色 邻点全和可区别全染色 邻点全和可区别全色数 

分 类 号：O157.5[理学—数学]