{
  "id": "1404.1651",
  "version": "v2",
  "published": "2014-04-07T03:51:05.000Z",
  "updated": "2015-07-01T06:11:39.000Z",
  "title": "Characterization of Line-Consistent Signed Graphs",
  "authors": [
    "Daniel C. Slilaty",
    "Thomas Zaslavsky"
  ],
  "comment": "5 pages. V2 defines sign of a walk and corrects statement of Theorem 4 (\"is balanced and\" was missing); also minor copyediting",
  "categories": [
    "math.CO"
  ],
  "abstract": "The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede's relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede's theorem as well as a structural description of line-consistent signed graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-07T03:51:05.000Z",
      "comment": "5 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-01T06:11:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C22"
    ],
    "keywords": [
      "line-consistent signed graphs",
      "characterization",
      "line graph",
      "signed edges carries vertex signs",
      "vertex-signed graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}