Analisis b-Coloring pada Keluarga Graf Roda

Abstract

This research aims to analyze the concept of b-coloring in graph theory, specifically within the family of wheel graphs. Graph coloring is an important concept in graph theory that involves assigning colors to the vertices of a graph in such a way that no two adjacent vertices share the same color. One aspect of graph coloring is b-coloring. b-Coloring is a method of coloring the vertices of a graph that ensures that each color class has at least one vertex that is adjacent to all other color classes. This study focuses on determining the b-chromatic number, which is the largest integer k that indicates a graph can be b-colored with k colors. The graphs examined in this research include Gear Graph (𝐺𝑛), Helm Graph (𝐻𝑛), Web Graph (𝑊𝑏𝑛), Flower Graph (𝐹𝑙𝑛), Sun Flower Graph (𝑆𝑓𝑛), and Lemon Graph (𝐿𝑒𝑛), with n ≥ 3.