For a simple undirected graph G with vertex set V and edge set E,a total k-labelingλ: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 weightsωt(x)andωt(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 nm[ ]∗ or nm[ ]∗ vertices is denoted by Tm,n. In this paper, the total vertex irregularity strength of equitable complete 7-partite graphs T7,n(n≠19)is given.%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 nm[]∗个顶点,或是具有 nm[]∗个顶点,则记为Tm,n 。本文给出了均匀完全7-部图T7,n(n≠19)的全非正规强度。
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