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) = Σ_{vϵN (u)}l(v). If for every uv ϵ E(G), w(u) ≠ w(v) and opt(l) = min(max(l_i); l_i 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 χ_lis(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.

Subject Classification:

• 05C15
• 05C78

Keywords:

• Local irregularity vertex coloring
• Chromatic number local irregular