On the total edge irregularity strength of some copies of ladder 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 defined by wf(uv) = f(u) + f(uv) + f(v) and denoted by by wf(uv) and. A total k-labeling of G is called edge irregular if every two distinct edges have distinct weight. The total edge irregularity strength of G is denoted by tes(G) and defined by the minimum k such that G has an edge irregular total k-labeling. The labeling was introduced by Bača et al. in 2007. In this paper, we determine the total edge irregularity strength of some copies of ladder graphs.