A note on vertex irregular total labeling of trees

Faisal Susanto, Rinovia Simanjuntak, Edy Tri Baskoro

Abstract


The total vertex irregularity strength of a graph G=(V,E) is the minimum integer k so that there is a mapping from V ∪ E to the set {1,2,...,k} so that the vertex-weights (i.e., the sum of labels of a vertex together with the edges incident to it) are all distinct. In this note, we present a new sufficient condition for a tree to have total vertex irregularity strength ⌈(n1+1)/2⌉, where n1 is the number of vertices of degree one in the tree.

Keywords


vertex irregular total $k$-labeling; total vertex irregularity strength; trees

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DOI: http://dx.doi.org/10.19184/ijc.2023.7.1.1

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