On edge irregularity strength of ladder related graphs

Abstract

For a simple graph G, a vertex labeling ? : V (G) ? {1, 2, . . . , k} is called k-labeling. The weight of an edge xy in G, written w?(xy), is the sum of the labels of end vertices x and y, i.e., w?(xy) = ?(x) + ?(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f, w?(e) 6= w?(f). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, written es(G). In this paper, we investigate the edge irregularity strength of ladder graph, triangular ladder graph, and diagonal ladder graph.