The b-Chromatic Colouring of Comb Product of Path Graphs and Wheel Graphs

A graph G's chromatic number \(\chi \left(G\right)\) characterizes the least number of colors required to appropriately color the points of a graph \(G\) so that no two adjoining points have the same color. In fact, the least number of colors required to color the points of a graph \(G\) is known as the b-chromatic number or \(\varphi (G),\) that no two spots separated by one or two distances obtain the same color. The b-chromatic number has applications in various fields like assignment problems, frequency allotment in wireless communication grid and resource allocation in computer networks, among others. It is a way of quantifying the complexity of colorings with specific adjacency constraints in graphs. Irving and Manlove introduced the idea of the b-chromatic number. The b-chromatic coloring of wheel graph and the comb product of path graphs are covered in this research paper.