Vol. LXXXII, 1 (2013)
p. 29 - 38

Total vertex irregularity strength of convex polytope graphs

O. Al-Mushayt, A. Arshad and M. K. Siddiqui

Received: February 2, 2012;   Accepted: September 18, 2012

Abstract.   A total vertex irregular k-labeling j 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.

Keywords:  Vertex irregular total k-labeling; total vertex irregularity strength; cycles, convex polytope graphs.  

AMS Subject classification: Primary:  05C78 

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
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