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Total vertex irregularity strength of convex polytope graphs

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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.
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