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On the total vertex irregularity strength of trees. (English) Zbl 1208.05014

Summary: A vertex irregular total \(k\)-labelling \(\lambda :V(G) \cup E(G) \to \{1,2,\dots ,k\}\) 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.

MSC:

05C05 Trees
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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References:

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