On Total Vertex Irregularity Strength Cocktail Party Graphs

Abstract

A vertex irregular total k-labeling of a graph G is a function λ from both the vertex and the edge sets to {1,2,3,,k} such that for every pair of distinct vertices u and x, λ(u)+ Σλ(uv) ≠ λ(x)+ Σλ(xy). The integer k is called the total vertex irregularity strength, denoted by tvs(G), is the minimum value of the largest label over all such irregular assignments. In this paper, we prove that the total vertex irregularity strength of the Cocktail Party graph H_2,n, that is tvs(H_2,n)= 3 for n≥3.