{
  "id": "math/0510296",
  "version": "v2",
  "published": "2005-10-14T09:04:49.000Z",
  "updated": "2007-08-16T20:12:51.000Z",
  "title": "Engel graph associated with a group",
  "authors": [
    "Alireza Abdollahi"
  ],
  "comment": "Proposition 2.8 is omitted however the proof is correct. Some errors and misprints are corrected. Corollary 2.11 (now Corollary 2.10) is now in a corrected form",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Let $G$ be a non-Engel group and let $L(G)$ be the set of all left Engel elements of $G$. Associate with $G$ a graph $\\mathcal{E}_G$ as follows: Take $G\\backslash L(G)$ as vertices of $\\mathcal{E}_G$ and join two distinct vertices $x$ and $y$ whenever $[x,_k y]\\not=1$ and $[y,_k x]\\not=1$ for all positive integers $k$. We call $\\mathcal{E}_G$, the Engel graph of $G$. In this paper we study the graph theoretical properties of $\\mathcal{E}_G$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-16T20:12:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F45",
      "20D60",
      "05C25"
    ],
    "keywords": [
      "engel graph",
      "left engel elements",
      "non-engel group",
      "distinct vertices",
      "graph theoretical properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}