On the Chromatic Number Local Irregularity of Related Wheel Graph

Abstract

A function f is called a local irregularity vertex coloring if (i) l : V (G) ! f1; 2; ; kg as vertex irregular k-labeling and w : V (G) ! N, for every uv 2 E(G); w(u) 6= w(v) where w(u) = v2N(u)l(v) and (ii) max(l) = minfmaxflig; livertex irregular labelingg. The chromatic number of local irregularity vertex coloring of G, denoted by lis(G), is the minimum cardinality of the largest label over all such local irregularity vertex coloring. In this article, we study the local irregularity vertex coloring of related wheel graphs and we have found the exact value of their chromatic number local irregularity, namely web graph, helm graph, close helm graph, gear graph, fan graph, sun let graph, and double wheel graph.