{
  "id": "2206.07381",
  "version": "v1",
  "published": "2022-06-15T08:44:31.000Z",
  "updated": "2022-06-15T08:44:31.000Z",
  "title": "Pancyclicity in the Cartesian Product $(K_9-C_9 )^n$",
  "authors": [
    "Syeda Afiya",
    "M Rajesh"
  ],
  "comment": "6 PAGES, 4 FIGURES",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A graph $G$ on $m$ vertices is pancyclic if it contains cycles of length $l$, $3\\leq l \\leq m$ as subgraphs in $G$. The complete graph $K_{9}$ on 9 vertices with a cycle $C_{9}$ of length 9 deleted from $K_{9}$ is denoted by $(K_{9}-C_{9})$. In this paper, we prove that $(K_{9}-C_{9})^{n}$, the Cartesian product of $(K_{9}-C_{9})$ taken $n$ times, is pancyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-15T08:44:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C45",
      "G.2"
    ],
    "keywords": [
      "cartesian product",
      "pancyclicity",
      "contains cycles",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}