{
  "id": "1406.6168",
  "version": "v2",
  "published": "2014-06-24T08:40:21.000Z",
  "updated": "2014-08-28T09:56:26.000Z",
  "title": "Total irregularity and $f^t$-irregularity of Jaco Graphs, $J_n(1), n \\in \\Bbb N$",
  "authors": [
    "Johan Kok"
  ],
  "comment": "11 pages. Minor typographical errors corrected. To be submitted to the \\emph{Pioneer Journal of Mathematics and Mathematical Sciences.}",
  "categories": [
    "math.CO"
  ],
  "abstract": "Total irregularity of a simple undirected graph $G$ is defined to be $irr_t(G) = \\frac{1}{2}\\sum\\limits_{u, v \\in V(G)}|d(u) - d(v)|$. See Abdo and Dimitrov [2]. We allocate the \\emph{Fibonacci weight,} $f_i$ to a vertex $v_j$ of a simple connected graph, if and only if $d(v_j) = i$ and define the \\emph{total fibonaccian irregularity} or $f_t-irregularity$ denoted $firr_t(G)$ for brevity, as: $firr_t(G) = \\sum\\limits_{i=1}^{n-1}\\sum\\limits_{j=i+1}^{n}|f_i - f_j|.$ The concept of an \\emph{edge-joint} is also introduced to be the simple undirected graph obtained from two simple undirected graphs $G$ and $H$ by linking the edge $vu_{v \\in V(G), u \\in V(H)}$. This paper presents results for the undirected underlying graphs of Jaco Graphs, $J_n(1)$. For more on Jaco Graphs $J_n(1)$ see [3]. Finally we pose an open problem with regards to $firr_t^\\pm(G).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-24T08:40:21.000Z",
      "comment": "11 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-28T09:56:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jaco graphs",
      "total irregularity",
      "simple undirected graph",
      "open problem",
      "fibonaccian irregularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.6168K"
    }
  }
}