{
  "id": "2007.11844",
  "version": "v1",
  "published": "2020-07-23T08:16:16.000Z",
  "updated": "2020-07-23T08:16:16.000Z",
  "title": "On graphs with some normalized Laplacian eigenvalue of extremal multiplicity",
  "authors": [
    "Fenglei Tian",
    "Junqing Cai",
    "Zuosong Liang",
    "Xuntuan Su"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected simple graph on $n$ vertices. Let $\\mathcal{L}(G)$ be the normalized Laplacian matrix of $G$ and $\\rho_{n-1}(G)$ be the second least eigenvalue of $\\mathcal{L}(G)$. Denote by $\\nu(G)$ the independence number of $G$. Recently, the paper [Characterization of graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$, arXiv:1912.13227] discussed the graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$. However, there is one remaining case (graphs with $\\rho_{n-1}(G)\\neq 1$ and $\\nu(G)= 2$) not considered. In this paper, we focus on cographs and graphs with diameter 3 to investigate the graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-23T08:16:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "normalized laplacian eigenvalue",
      "extremal multiplicity",
      "connected simple graph",
      "independence number",
      "normalized laplacian matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}