{
  "id": "2003.09602",
  "version": "v1",
  "published": "2020-03-21T07:52:28.000Z",
  "updated": "2020-03-21T07:52:28.000Z",
  "title": "The Number of Perfect Matchings in Möbius Ladders and Prisms",
  "authors": [
    "R. S. Lekshmi",
    "Douglas B. West"
  ],
  "comment": "5 pages, No Figures, 16 References. Research supported by National Natural Science Foundation of China grants NNSFC 11871439 and 11971439",
  "categories": [
    "math.CO"
  ],
  "abstract": "The 1970s conjecture of Lov\\'asz and Plummer that the number of perfect matchings in any $3$-regular graph is exponential in the number of vertices was proved in 2011 by Esperet, Kardo\\v{s}, King, Kr\\'al', and Norine. We give the exact formula for the number of perfect matchings in two families of $3$-regular graphs. In the graph consisting of a $2n$-cycle with diametric chords (also known as the M\\\"obius ladder $M_n$ and a Harary graph) and in the cartesian product of the cycle $C_n$ with an edge (called the cycle prism), the number of matchings is the sum of the Fibonacci numbers $F_{n-1}$ and $F_{n+1}$, plus two more for the M\\\"obius ladder when $n$ is odd and for the cycle prism when $n$ is even.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-21T07:52:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "perfect matchings",
      "möbius ladders",
      "regular graph",
      "cycle prism",
      "1970s conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}