On local irregularity vertex coloring of comb product on star graphs

Abstract

Let G = (V,E) be a graph with vertex set V and edge set E. The graph G is said to be a local irregular vertex coloring if there is a function f is a called a local irregularity vertex coloring if : (i) l : (V (G)) ? {1, 2,...,k} as a vertex irregular k-labeling and w : V(G) ? N, for every uv ? E(G),w(u) = w(v) where w(u) = Sv?N(u) l(i) and (ii) opt (I) = min{rnax{li; livertex irregular labeling}}. The chromatic number of local irregularity vertex coloring of G denoted by Xlis(G), is the minimum cardinality of the largest label over all such local irregularity vertex coloring. In this paper, we study local irregular vertex coloring of G ?° Sn when G is complete bipartite graph (Km,p), ladder graph (Lm), fan graph (Fm), friendship graph (Frm), and cycle graph (Cm).