{
  "id": "1304.0081",
  "version": "v1",
  "published": "2013-03-30T10:06:37.000Z",
  "updated": "2013-03-30T10:06:37.000Z",
  "title": "Coloring of a Digraph",
  "authors": [
    "E. Sampathkumar"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "\\qquad A \\emph{coloring} of a digraph $D=(V,E)$ is a coloring of its vertices following the rule: Let $uv$ be an arc in $D$. If the tail $u$ is colored first, then the head $v$ should receive a color different from that of $u$. The \\emph{dichromatic number} $\\chi_d(D)$ of $D$ is the minimum number of colors needed in a coloring of $D$. Besides obtaining many results and bounds for $\\chi_d(D)$ analogous to that of chromatic number of a graph, we prove $\\chi_d(D)=1$ if $D$ is acyclic. New notions of sequential colorings of graphs/digraphs are introduced. A characterization of acyclic digraph is obtained interms of $L$-matrix of a vertex labeled digraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-30T10:06:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "acyclic digraph",
      "sequential colorings",
      "minimum number",
      "chromatic number",
      "vertex labeled digraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0081S"
    }
  }
}