On the total vertex irregularity strength of firecracker graph
Arum Haryanti, Diari Indriati, Till Martini · Journal of Physics Conference Series · 2019
Let G be a connected graph with vertex set V ( G ) and edge set E ( G ). A total k -labeling is a labeling . A vertex irregular total k -labeling of a graph G ( V; E ) is a total k -labeling such that the weight for all vertices is distinct. The weight of vertex u in G , denoted by wt ( u ), is defined as the sum of the label of vertex u and the label of all edges incident with the vertex u . Total vertex irregularity strength of G denoted by tvs ( G ), is the minimum value of the largest label k over all such vertex irregular total k -labeling. The firecracker graph is a graph obtained by the concatenation of mn -stars by linking one leaf from each. In this paper, we investigate the total vertex irregularity strength of firecracker graphs, for n = 1, 2 and m > 1. For n = 1 and m > 1. For n = 2 and m > 1, is defined into 2 formulas; for 2 ≤ m ≤ 8 and for m ≥ 9.