Local irregular vertex coloring of some families graph

Abstract

All graph in this paper is connected and simple graph. Let d(u, v) be a distance between any vertex u and v in graph G = (V, E). A function l : V(G) → {1, 2, ..., k} is called vertex irregular k-labelling and w : V(G) → N where w(u) = ΣvϵN (u)l(v). If for every uv ϵ E(G), w(u) ≠ w(v) and opt(l) = min(max(li); li vertex irregular labelling) is called a local irregularity vertex coloring. The minimum cardinality of the largest label over all such local irregularity vertex coloring is called chromatic number local irregular, denoted by χlis(G). In this paper, we study about local irregularity vertex coloring of families graphs, namely triangular book graph, square book graph, pan graph, subdivision of pan graph, and grid graphs.