{
  "id": "2303.10488",
  "version": "v1",
  "published": "2023-03-18T19:56:23.000Z",
  "updated": "2023-03-18T19:56:23.000Z",
  "title": "Subdivision and Graph Eigenvalues",
  "authors": [
    "Hitesh Kumar",
    "Bojan Mohar",
    "Shivaramakrishna Pragada",
    "Hanmeng Zhan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the $k$-th largest and $k$-th smallest eigenvalues for any fixed $k$. It is expected that after subdivision, most eigenvalues of the new graph will lie in the interval $[-2,2]$. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-18T19:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "graph eigenvalues",
      "subdivision",
      "th smallest eigenvalues",
      "graph outside",
      "asymptotic nature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}