ON EDGE IRREGULARITY STRENGTH OF LADDER RELATED GRAPHS

For a simple graph G, a vertex labeling phi : V(G) -> {1, 2, ... , k} is called k-labeling. The weight of an edge xy in G, written w phi(xy), is the sum of the labels of end vertices x and y, i.e., w phi(xy) = phi(x) + phi(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 phi(e) =6 w phi(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.