# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

S. Francis Raj and M. Gokulnath

Title:

b-coloring of the Mycielskian of some classes of graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-02-11, Revised: 2019-10-31, Accepted: 2019-11-02, https://doi.org/10.7151/dmgt.2265

Abstract:

The b-chromatic number $b(G)$ of a graph $G$ is the maximum $k$ for which $G$ has a proper vertex coloring using $k$ colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we have mainly investigated on the b-chromatic number of the Mycielskian of regular graphs. In particular, we have obtained the exact value of the b-chromatic number of the Mycielskian of some classes of graphs. This includes a few families of regular graphs, graphs with $b(G)=2$ and split graphs. In addition, we have found bounds for the b-chromatic number of the Mycielskian of some more families of regular graphs in terms of the b-chromatic number of their original graphs. Also we have found b-chromatic number of the generalized Mycielskian of some regular graphs.

Keywords:

b-coloring, b-chromatic number, Mycielskian of graphs, regular graphs