{
  "id": "2004.14526",
  "version": "v1",
  "published": "2020-04-30T00:25:18.000Z",
  "updated": "2020-04-30T00:25:18.000Z",
  "title": "On the Connectivity of Token Graphs of Trees",
  "authors": [
    "Ruy Fabila-Monroy",
    "Jesús Leaños",
    "Ana Laura Trujillo-Negrete"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $k$ and $n$ be integers such that $1\\leq k \\leq n-1$, and let $G$ be a simple graph of order $n$. The $k$--token graph $F_k(G)$ of $G$ is the graph whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent in $F_k(G)$ whenever their symmetric difference is an edge of $G$. In this paper we show that if $G$ is a tree, then the connectivity of $F_k(G)$ is equal to the minimum degree of $F_k(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-30T00:25:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "token graph",
      "connectivity",
      "simple graph",
      "symmetric difference",
      "minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}