Total edge irregularity strength for three classes of graphs

Abstract

A total edge-irregular k-labeling V(G) ∩ E(G)-> {l,2,...,k} of a graph G is a labeling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct, where the weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labeling is called the total edge irregularity strength of G, tes(G). In this paper we find the tes for the graphs En, Fn and Pa,b.