{
  "id": "1707.02039",
  "version": "v1",
  "published": "2017-07-07T05:29:09.000Z",
  "updated": "2017-07-07T05:29:09.000Z",
  "title": "A note on some variations of the $γ$-graph",
  "authors": [
    "C. M. Mynhardt",
    "L. E. Teshima"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G$, the $\\gamma$-graph of $G$, $G(\\gamma)$, is the graph whose vertices correspond to the minimum dominating sets of $G$, and where two vertices of $G(\\gamma)$ are adjacent if and only if their corresponding dominating sets in $G$ differ by exactly two adjacent vertices. In this paper, we present several variations of the $\\gamma$-graph including those using identifying codes, locating-domination, total-domination, paired-domination, and the upper-domination number. For each, we show that for any graph $H$, there exist infinitely many graphs whose $\\gamma$-graph variant is isomorphic to $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-07T05:29:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variations",
      "graph variant",
      "minimum dominating sets",
      "adjacent vertices",
      "upper-domination number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}