{
  "id": "1902.02608",
  "version": "v1",
  "published": "2019-02-07T13:18:34.000Z",
  "updated": "2019-02-07T13:18:34.000Z",
  "title": "Spectra of eccentricity matrices of graphs",
  "authors": [
    "Iswar Mahato",
    "R. Gurusamy",
    "M. Rajesh Kannan",
    "S. Arockiaraj"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.CO",
    "math.SP"
  ],
  "abstract": "The eccentricity matrix of a connected graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and setting the remaining entries as $0$. In this article, a conjecture about the least eigenvalue of eccentricity matrices of trees, presented in the article [Jianfeng Wang, Mei Lu, Francesco Belardo, Milan Randic. The anti-adjacency matrix of a graph: Eccentricity matrix. Discrete Applied Mathematics, 251: 299-309, 2018.], is solved affirmatively. In addition to this, the spectra and the inertia of eccentricity matrices of various classes of graphs are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-07T13:18:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C50"
    ],
    "keywords": [
      "eccentricity matrix",
      "jianfeng wang",
      "distance matrix",
      "anti-adjacency matrix",
      "largest distances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}