On vertex irregular total labelings of convex polytope graphs

Abstract

A vertex irregular total labeling Φ of a graph G is a labeling of vertices and edges of G with labels from the set {1,2,...,k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x in G is the sum of its label and the labels of all edges incident with a given vertex x. The minimum k for which the graph G has a vertex irregular total labeling is called the total vertex irregularity strength of G. In this paper, we study the total vertex irregularity strength of convex polytope A_n, R_n,Q _n, M_n graphs.