On the local irregularity vertex coloring of volcano, broom, parachute, double broom and complete multipartite graphs
Arika Indah Kristiana, Nafidatun Nikmah, Dafik Dafik, Ridho Alfarisi, Moh. Hasan, Slamin Slamin · Discrete Mathematics Algorithms and Applications · 2021
Let [Formula: see text] be a simple, finite, undirected, and connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bijection [Formula: see text] is label function [Formula: see text] if [Formula: see text] and for any two adjacent vertices [Formula: see text] and [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] is set of vertices adjacent to [Formula: see text]. [Formula: see text] is called local irregularity vertex coloring. The minimum cardinality of local irregularity vertex coloring of [Formula: see text] is called chromatic number local irregular denoted by [Formula: see text]. In this paper, we verify the exact values of volcano, broom, parachute, double broom and complete multipartite graphs.