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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