Bounds for the b-chromatic number of powers of hypercubes
Abstract
The b-chromatic number of a graph is the maximum for which has a proper vertex coloring using colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we mainly investigate on one of the open problems given in [P. Francis, S. Francis Raj, On b-coloring of powers of hypercubes, Discrete Appl. Math. 225 (2017) 74-86.]. As a consequence, we have obtained an upper bound for the b-chromatic number of some powers of hypercubes. This turns out to be an improvement of the already existing bound in [P. Francis, S. Francis Raj, On b-coloring of powers of hypercubes, Discrete Appl. Math. 225 (2017) 74-86.]. Further, we have determined a lower bound for the b-chromatic number of some powers of the Hamming graph, a generalization of the hypercube.
Cite
@article{arxiv.2101.11886,
title = {Bounds for the b-chromatic number of powers of hypercubes},
author = {P. Francis and S. Francis Raj and M. Gokulnath},
journal= {arXiv preprint arXiv:2101.11886},
year = {2021}
}