The $b$-Chromatic Number of Certain Graphs and Digraphs

TL;DR

This paper investigates the $b$-chromatic number for specific classes of graphs and digraphs, introduces Chithra graphs, and explores their properties.

Contribution

It introduces Chithra graphs as a new family and analyzes the $b$-chromatic number within these and other graph classes.

Findings

Determined $b$-chromatic numbers for certain graph classes

Defined and studied properties of Chithra graphs

Extended understanding of $b$-chromatic number in digraphs

Abstract

The studies on $b$-chromatic number attracted much interest since its introduction. In this paper, we discuss the $b$-chromatic number of certain classes of graphs and digraphs. The notion of a new general family of graphs called the Chithra graphs of a graph $G$ are also introduced.