{
  "id": "1304.0083",
  "version": "v1",
  "published": "2013-03-30T10:13:00.000Z",
  "updated": "2013-03-30T10:13:00.000Z",
  "title": "Characterizations of 2-Colorable (Bipartite) and 3-Colorable Graphs",
  "authors": [
    "E. Sampathkumar",
    "M. A. Sriraj"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A \\emph{directional labeling} of an edge $\\emph{uv}$ in a graph $G=(V,E)$ by an ordered pair $ab$ is a labeling of the edge $uv$ such that the label on $uv$ in the direction from $u$ to $v$ is $\\ell(uv)=ab$, and $\\ell(vu)=ba$. New characterizations of 2-colorable (bipartite) and 3-colorable graphs are obtained in terms of directional labeling of edges of a graph by ordered pairs $ab$ and $ba$. In addition we obtain characterizations of 2-colorable and 3-colorable graphs in terms of matrices called directional adjacency matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-30T10:13:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterizations",
      "ordered pair",
      "directional adjacency matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0083S"
    }
  }
}