On the edge irregularity strength of grid graphs

Abstract

For a simple graph G, a vertex labeling ϕ:V(G)→{1,2,…,k} is called a vertex k-labeling. For any edge xy in G, its weight wϕ(xy)=ϕ(x)+ϕ(y). If all the edge weights are distinct, then ϕ is called an edge irregular k-labeling of G. The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G).In this paper, we determine an exact value of edge irregularity strength for triangular grid graph Lnm, zigzag graph Znm and Cartesian product Pn□Pm□P2.