{
  "id": "2209.04204",
  "version": "v1",
  "published": "2022-09-09T09:38:22.000Z",
  "updated": "2022-09-09T09:38:22.000Z",
  "title": "Hamiltonian Complete Number of Some Variants of Caterpillar Graphs",
  "authors": [
    "Tayo Charles Adefokun",
    "Kingsley Nosa Onaiwu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph G is said to be Hamiltonian if it contains a spanning cycle. In other words, G contains a cycle that passes through all the the vertices in the vertex set V(G) of G. A graph that does not contain a spanning cycle is a non-Hamiltonian graph. In this work, we investigate the the Hamiltonian completeness of certain trees. The Hamiltonian complete number of G, a non-Hamiltonian graph is the optimal number of edges that if added to the edge set E(G) of G, then G becomes Hamiltonian. Our focus is on certain classes of caterpillar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-09T09:38:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C40",
      "05C38"
    ],
    "keywords": [
      "hamiltonian complete number",
      "caterpillar graphs",
      "non-hamiltonian graph",
      "spanning cycle",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}