{
  "id": "1607.00473",
  "version": "v1",
  "published": "2016-07-02T07:32:11.000Z",
  "updated": "2016-07-02T07:32:11.000Z",
  "title": "Distance and distance signless Laplacian spread of connected graphs",
  "authors": [
    "Lihua You",
    "Liyong Ren",
    "Guanglong Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a connected graph $G$ on $n$ vertices, recall that the distance signless Laplacian matrix of $G$ is defined to be $\\mathcal{Q}(G)=Tr(G)+\\mathcal{D}(G)$, where $\\mathcal{D}(G)$ is the distance matrix, $Tr(G)=diag(D_1, D_2, \\ldots, D_n)$ and $D_{i}$ is the row sum of $\\mathcal{D}(G)$ corresponding to vertex $v_{i}$. Denote by $\\rho^{\\mathcal{D}}(G),$ $\\rho_{min}^{\\mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $\\mathcal{D}(G)$, respectively. And denote by $q^{\\mathcal{D}}(G)$, $q_{min}^{\\mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $\\mathcal{Q}(G)$, respectively. The distance spread of a graph $G$ is defined as $S_{\\mathcal{D}}(G)=\\rho^{\\mathcal{D}}(G)- \\rho_{min}^{\\mathcal{D}}(G)$, and the distance signless Laplacian spread of a graph $G$ is defined as $S_{\\mathcal{Q}}(G)=q^{\\mathcal{D}}(G)-q_{min}^{\\mathcal{D}}(G)$. In this paper, we point out an error in the result of Theorem 2.4 in \"Distance spectral spread of a graph\" [G.L. Yu, et al, Discrete Applied Mathematics. 160 (2012) 2474--2478] and rectify it. As well, we obtain some lower bounds on ddistance signless Laplacian spread of a graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-02T07:32:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "connected graph",
      "largest eigenvalue",
      "ddistance signless laplacian spread",
      "distance spectral spread",
      "distance signless laplacian matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}