{
  "id": "2505.04314",
  "version": "v1",
  "published": "2025-05-07T10:59:06.000Z",
  "updated": "2025-05-07T10:59:06.000Z",
  "title": "Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter $3$",
  "authors": [
    "Shiping Liu",
    "Heng Zhang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO",
    "math.SP"
  ],
  "abstract": "We prove the monotonic normalized heat diffusion property on distance-regular graphs with classical parameters of diameter $3$. Regev and Shinkar found a Cayley graph for which this property fails. On the other hand, this property has been proved on abelian Cayley graphs, graphs with $3$ distinct eigenvalues and regular bipartite graphs with $4$ distinct eigenvalues by Price, Nica and Kubo-Namba, respectively. A distance regular graph with classical parameters of diameter $3$ has $4$ distinct eigenvalues and is not necessarily bipartite or vertex transitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-07T10:59:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical parameters",
      "distance-regular graphs",
      "distinct eigenvalues",
      "cayley graph",
      "monotonic normalized heat diffusion property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}