On The Total Edge Irregularity Strength of Some Copies of Books Graphs

Abstract

Let G = (V(G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f : V(G) ∪ E(G) → {1,2, …, k}. The edge weight uv under the labeling f is denoted by Wf (uv) and defined by wf (uv) = f(u) + f(uv) + f(v). A total k -labeling of G is called edge irregular if there are no two edges with the same weight. The total edge irregularity strength of G, denoted by tes (G), is the minimum k such that G has an edge irregular total k-labeling. The labeling was introduced by Bača, Jendroľ, Miller, and Ryan in 2007. In this paper, we determine the total edge irregularity strength of some copies of book graphs.