LOCAL IRREGULARITY POINT COLORING ON THE RESULT OF SUBDIVISION OPERATION OF HELM GRAPHS

Abstract

 One of the sub-chapters studied in graphs is local irregularity vertex coloring of graph. The based on definition of local irregularity vertex coloring of graph, as follow : (i)l : V (G) →{1, 2, 3, . . . , k} as a vertex irregular labeling and w : V (G) → N, for every uv ∈ E(G), w(u) ̸=w(v) with w(u) = Pv∈N(u)l(v) and (i) Opt(l) = min{max(li); li is a vertex irregular labeling}. The chromatic number of the local irregularity vertex coloring of G denoted by χlis(G), is the minimum cardinality of the largest label over all such local irregularity vertex colorings. In this article, discuss about local irregularity vertex coloring of subdivision by helm graph (Sg(Hn)).