On the Local Irregularity Vertex Coloring of Related Grid Graph

Abstract

All graph in this paper is connected and simple graph. Let graph d(u,v) be a distance between any vertex u and v in graph ( ). A functio ( ) * +n is called vertex irregular k-labelling and ( ) where ( ) ∑ ( ) ( ) If for every ( ) ( ) ( ) and maks(l) = min{maks{li}; li , vertex irregular labelling} is called a local irregularity vertex coloring. χlis(G) or chromatic number of local irregularity vertex coloring of graph (G) is the minimum cardinality of the largest label over all such local irregularity vertex coloring. In this paper, we will study about local irregularity vertex coloring of related grid graphs, and we have found the exact value of their chromatic number local irregularity, namely ladder graph, triangular ladder graph, and H-graph.