Total absolute difference edge irregularity strength of some families of graphs

Abstract

A total labeling ? is defined to be an edge irregular total absolute difference k-labeling of the graph G if for every two different edges e and f of G there is wt(e) ? wt(f) where weight of an edge e = xy is defined as wt(e) = |?(e) ? ?(x) ? ?(y)|. The minimum k for which the graph G has an edge irregular total absolute difference labeling is called the total absolute difference edge irregularity strength of the graph G, tades(G). In this paper, we determine the total absolute difference edge irregularity strength of the precise values for some families of graphs.