{
  "id": "1404.0484",
  "version": "v1",
  "published": "2014-04-02T08:37:41.000Z",
  "updated": "2014-04-02T08:37:41.000Z",
  "title": "Characteristics of Finite Jaco Graphs, $J_n(1), n \\in \\Bbb N$",
  "authors": [
    "Johan Kok",
    "Paul Fisher",
    "Bettina Wilkens",
    "Mokhwetha Mabula",
    "Vivian Mukungunugwa"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce the concept of a family of finite directed graphs (order 1) which are directed graphs derived from an infinite directed graph (order 1), called the 1-root digraph. The 1-root digraph has four fundamental properties which are; $V(J_\\infty(1)) = \\{v_i|i \\in \\Bbb N\\}$ and, if $v_j$ is the head of an edge (arc) then the tail is always a vertex $v_i, i<j$ and, if $v_k$, for smallest $k \\in \\Bbb N$ is a tail vertex then all vertices $v_\\ell, k< \\ell <j$ are tails of arcs to $v_j$ and finally, the degree of vertex $k$ is $d(v_k) = k.$ The family of finite directed graphs are those limited to $n \\in \\Bbb N$ vertices by lobbing off all vertices (and edges arcing to vertices) $v_t, t> n.$ Hence, trivially we have $d(v_i) \\leq i$ for $i \\in \\Bbb N$. We present an interesting Fibonaccian-Zeckendorf result and present the Fisher Algorithm to table particular values of interest. It is meant to be an introductory paper to encourage exploratory research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-02T08:37:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite jaco graphs",
      "finite directed graphs",
      "characteristics",
      "encourage exploratory research",
      "infinite directed graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0484K"
    }
  }
}