Total vertex irregularity strength of certain equitable complete m-partite graphs

For a simple undirected graph G with vertex set V and edge set E, a total k labeling lambda : V boolean OR 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 wt(x) and wt(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 on n vertices in which each part has either left perpendicularn/mleft perpendicular or inverted right perpendicularn/minverted right perpendicula r vertices is denoted by T-m,T-n. The total vertex irregularity strength of some equitable complete m partite graphs, namely, T-m,T-m+1, T-m,T-m+2, T-m,T-2m, T-m,T-2m+1, T-m,T-3m-1 (m >= 4), T-m,T-n (n = 3m + r,r = 1,2, ..., m - 1), and equitable complete 3-partite graphs have been studied in this paper.