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

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 W f ( uv ) and defined by w f ( 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.