{
  "id": "2101.01855",
  "version": "v1",
  "published": "2021-01-06T03:45:18.000Z",
  "updated": "2021-01-06T03:45:18.000Z",
  "title": "Hamiltonicity of the Token Graphs of some Join Graphs",
  "authors": [
    "Luis Adame",
    "Luis Manuel Rivera",
    "Ana Laura Trujillo-Negrete"
  ],
  "comment": "The results presented in this article generalize some results presented in arXiv:2007.00115",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a simple graph of order $n$ and let $k$ be an integer such that $1\\leq k\\leq n-1$. The $k$-token graph $G^{\\{k\\}}$ of $G$ is the graph whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent in $G^{\\{k\\}}$ whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper we study the Hamiltonicity of the $k$-token graphs of some join graphs. As a consequence, we provide an infinite family of graphs (containing Hamiltonian and non-Hamiltonian graphs) for which their $k$-token graphs are Hamiltonian. Our result provides, to our knowledge, the first family of non-Hamiltonian graphs for which their $k$-token graphs are Hamiltonian, for $2<k<n-2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T03:45:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C76"
    ],
    "keywords": [
      "token graph",
      "join graphs",
      "hamiltonicity",
      "non-hamiltonian graphs",
      "symmetric difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}