ON EDGE IRREGULARITY STRENGTH OF LADDER RELATED GRAPHS

ON EDGE IRREGULARITY STRENGTH OF LADDER RELATED GRAPHS

U. Salma, H. M. Nagesh

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Abstract

For a simple graph G, a vertex labeling   : V (G) ! f1; 2; : : : ; kg 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 de ned to be an edge irregular k-labeling of the graph G if for every two di erent 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.

Keywords

Irregularity strength, edge irregularity strength, ladder graphs, triangular ladder graphs, diagonal ladder graphs.