Elsevier

Discrete Mathematics

Volume 310, Issue 21, 6 November 2010, Pages 3043-3048
Discrete Mathematics

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On the total vertex irregularity strength of trees

https://doi.org/10.1016/j.disc.2010.06.041Get rights and content
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Abstract

A vertex irregular total k-labelling λ:V(G)E(G){1,2,,k} of a graph G is a labelling of vertices and edges of G done in such a way that for any different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The minimum k for which a graph G has a vertex irregular total k-labelling is called the total vertex irregularity strength of G, denoted by tvs(G). In this paper, we determine the total vertex irregularity strength of trees.

Keywords

Total vertex irregularity strength
Trees

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