均匀完全7-部图的全非正规强度  

Total vertex irregularity strength of equitable complete 7-partite graphs

作　　者：陈祥恩[1] 魏玉琼[1] 祁丽娟[2] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]兰州工业学院基础学科部,甘肃兰州730050

出　　处：《西北师范大学学报（自然科学版）》2017年第1期22-31,共10页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61163037;61163054;61363060)

摘　　要：简单图G的一个k-全标号λ:V∪E—→{1,2,…,k}称为点的全非正规k-标号,如果对于图G的任意两个不同的点x和y,它们的权wt(x)和wt(y)是不同的,其中图G的某个点x的权wt(x)是指点x的标号以及与x相关联的所有边的标号之和.图G的点的全非正规强度是使得G具有点的全非正规k-标号的最小正整数k,用tvs(G)表示.具有n个顶点的完全m-部图,如果它的每一部分或是具有[n/m]*个顶点,或是具有[n/m]*个顶点,则记为T_(m,n).本文给出了均匀完全7-部图T_7,n(n≠19)的全非正规强度.For a simple undirected graph G with vertex set V and edge set E, a total k-labeling λ：V∪E-→{1,2,…,k}is called a vertex irregular total k-labeling of G, if for every two distinct vertices x and y of G, their weights oot（x） and ωt（y） are distinct, where the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The total vertex irregularity strength of G, denoted by tvs（G）, is the minimum k for which the graph G has a vertex irregular total k-labeling.The complete m-partite graph with n vertices in which each part has either vertices isdenoted by T In this paper, the total vertex irregularity strength of equitable complete 7-partite graphsT7,n（n≠19） is given.

关 键 词：全非正规k-标号 权 全非正规强度 均匀完全7-部图 

分 类 号：O157.5[理学—数学]