Total edge irregularity strength of quadruplet and quintuplet book graphs

Abstract

Let G= (V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labelling is a function f : V ᴗE → {1,2,…,k} such that for any two different edges xy and x’y’ in E, their weights are distinct. The weight of edge xy is the sum of label of edge xy, labels of vertex x and of vertex y. The minimum k for which the graph G admits an edge irregular total k-labelling is called the total edge irregularity strength of G, denoted by tes(G). We have determined the total edge irregularity strength of book graphs, double book graphs and triple book graphs. In this paper, we show the exact value of the total edge irregularity strength of quadruplet book graphs and quintuplet book graphs.