Total Edge Irregularity Strength of Arithmetic Book Graphs

Abstract

For any simple undirected graph G(V, E), a map f : V ⋃ E → {1, 2, …, k} such that for any different edges xy and x’y’ their weights are distinct is called an edge irregular total k-labeling. The weight of edge xy is defined as the sum of edge label of xy, vertex label of x and vertex label of y. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G and is denoted by tes(G). In this paper, we determine the exact value of the total edge irregularity strength of odd arithmetic book graph Bn(C3, 5, 7, …2n+1) and even arithmetic book graph Bn(C4, 6, 8, …, 2n+2) of n sheets. We found that the tes of odd arithmetic book graph Bn(C3, 5, 7, …, 2n+1) of n sheets is equal to the ceiling function of and the tes of even arithmetic book graph Bn(C4, 6, 8, …, 2n+2) is equal to the ceiling function of .