{
  "id": "1510.00424",
  "version": "v1",
  "published": "2015-10-01T20:58:18.000Z",
  "updated": "2015-10-01T20:58:18.000Z",
  "title": "Regularity and Planarity of Token Graphs",
  "authors": [
    "Walter Carballosa",
    "Ruy Fabila-Monroy",
    "Jesús Leaños",
    "Luis Manuel Rivera"
  ],
  "comment": "13 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a graph of order $n$ and let $1\\leq k< n$ be an integer. The $k$-token graph of $G$ is the graph whose vertices are all the $k$-subsets of $V$, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper we characterize precisely, for each value of $k$, which graphs have a regular $k$-token graph and which connected graphs have a planar $k$-token graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T20:58:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C69"
    ],
    "keywords": [
      "token graph",
      "regularity",
      "symmetric difference",
      "adjacent vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}