On the total edge irregularity strength of generalized helm

Abstract

A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2,…, k}. An edge irregular total k-labeling of a graph G is a total k-labeling such that the weights calculated for all edges are distinct. The weight of an edge uv in G is defined as the sum of the label of u, the label of v and the label of uv. The total edge irregularity strength of G, denoted by tes(G), is the minimum value of the largest label k over all such edge irregular total k-labelings. In this paper, we investigate the total edge irregularity strength of generalized helm, Hmn for n ≥ 3, m = 1, 2, and m ≡ 0 (mod 3).