**Author(s):**O. Al-Mushayt | A. Arshad | M. K. Siddiqui

**Journal:**Acta Mathematica Universitatis Comenianae

ISSN 0862-9544

**Volume:**LXXXII;

**Issue:**1;

**Start page:**29;

**Date:**2013;

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**Keywords:**Vertex irregular total

*k*-labeling | total vertex irregularity strength | cycles | convex polytope graphs.

**ABSTRACT**

A total vertex irregular

*k*-labeling φ of a graph

*G*is a labeling of the 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. Here, 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 minimum

*k*for which the graph

*G*has a vertex irregular total

*k*-labeling is called the

*total vertex irregularity strength*of

*G*.We have determined an exact value of the total vertex irregularity strength of some convex polytope graphs.