On Total Edge Irregularity Strength of Generalized Web Graphs and Related Graphs

Abstract

Let G = (V, E) be a simple, connected and undirected graph with non empty vertex set V and edge set E. An edge irregular total k-labeling \({f: V(G)\cup E(G) \to \{ 1,2, \ldots, k \}}\) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights f(x) + f(xy) + f(y) and f(x′) + f(x′y′) + f(y′) are distinct. A total edge irregularity strength of graph G, denoted by tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we determine the exact value of the total edge irregularity strength of the generalized web graph W(n, m) and two families of related graphs.