A note on vertex irregular total labeling of trees - Faisal Susanto; Rinovia Simanjuntak; Edy Tri Baskoro (Indonesian Combinatorial Society (InaCombS), 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.