Total edge irregularity strength of book graphs and double 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-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).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-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).