{
  "id": "0704.1493",
  "version": "v3",
  "published": "2007-04-11T21:35:09.000Z",
  "updated": "2008-10-20T20:06:08.000Z",
  "title": "On a {K_4,K_{2,2,2}}-ultrahomogeneous graph",
  "authors": [
    "Italo J. Dejter"
  ],
  "comment": "12 pages, 4 figures",
  "journal": "Australasian Jour. of Combinatorics, 44 (2009), 63--75",
  "categories": [
    "math.CO"
  ],
  "abstract": "The existence of a connected 12-regular $\\{K_4,K_{2,2,2}\\}$-ultrahomogeneous graph $G$ is established, (i.e. each isomorphism between two copies of $K_4$ or $K_{2,2,2}$ in $G$ extends to an automorphism of $G$), with the 42 ordered lines of the Fano plane taken as vertices. This graph $G$ can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of $K_4$ and as the edge-disjoint union of 21 induced copies of $K_{2,2,2}$, with no more copies of $K_4$ or $K_{2,2,2}$ existing in $G$. Moreover, each edge of $G$ is shared by exactly one copy of $K_4$ and one of $K_{2,2,2}$. While the line graphs of $d$-cubes, ($3\\le d\\in\\ZZ$), are $\\{K_d, K_{2,2}\\}$-ultrahomogeneous, $G$ is not even line-graphical. In addition, the chordless 6-cycles of $G$ are seen to play an interesting role and some self-dual configurations associated to $G$ with 2-arc-transitive, arc-transitive and semisymmetric Levi graphs are considered.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-20T20:06:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C62"
    ],
    "keywords": [
      "edge-disjoint union",
      "semisymmetric levi graphs",
      "fano plane taken",
      "induced copies",
      "self-dual configurations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.1493D"
    }
  }
}