ON EDGE IRREGULARITY STRENGTH OF LADDER RELATED GRAPHS

For a simple graph G, a vertex labeling [phi] : V(G) [right arrow] {1, 2,..., k} is called k-labeling. The weight of an edge xy in G, written [W.sub.[phi]] (xy), is the sum of the labels of end vertices x and y, i.e., [W.sub.[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.sub.[phi]] (e) [not equal to] [W.sub.[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. Keywords: Irregularity strength, edge irregularity strength, ladder graphs, triangular ladder graphs, diagonal ladder graphs. AMS Subject Classification: 05C05, 05C45.