{
  "id": "2101.11886",
  "version": "v1",
  "published": "2021-01-28T09:30:13.000Z",
  "updated": "2021-01-28T09:30:13.000Z",
  "title": "Bounds for the b-chromatic number of powers of hypercubes",
  "authors": [
    "P. Francis",
    "S. Francis Raj",
    "M. Gokulnath"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "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 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-28T09:30:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "b-chromatic number",
      "francis raj",
      "discrete appl",
      "color class contains",
      "vertex adjacent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}