Total edge irregularity strength of ladder-related graphs

An edge irregular total k-labeling on simple and undirected graph G(V,E) is a map f:V∪E→{1,2,…,k} such that for any different edge xy and x'y' their weights f(x)+f(xy)+f(y) and f(x')+f(x'y')+f(y') are distinct. 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 families of ladder-related graphs, namely triangular ladder graphs, diagonal ladder graphs and circular triangular ladder graphs.