{
  "id": "2012.11880",
  "version": "v1",
  "published": "2020-12-22T08:36:40.000Z",
  "updated": "2020-12-22T08:36:40.000Z",
  "title": "The adjacency matrices and the transition matrices related to random walks on graphs",
  "authors": [
    "Tomohiro Ikkai",
    "Hiromichi Ohno",
    "Yusuke Sawada"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "A pointed graph $(\\Gamma,v_0)$ induces a family of transition matrices in Wildberger's construction of a hermitian hypergroup via a random walk on $\\Gamma$ starting from $v_0$. We will give a necessary condition for producing a hermitian hypergroup as we assume a weaker condition than the distance-regularity for $(\\Gamma,v_0)$. The condition obtained in this paper connects the transition matrices and the adjacency matrices associated with $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-22T08:36:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transition matrices",
      "random walk",
      "adjacency matrices",
      "hermitian hypergroup",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}