A note on vertex irregular total labeling of trees

Faisal Susanto (Institut Teknologi Bandung)
Rinovia Simanjuntak (Institut Teknologi Bandung)
Edy Tri Baskoro (Institut Teknologi Bandung)

Indonesian Journal of Combinatorics
Vol 7, No 1 (2023)

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.