{
  "id": "1505.07651",
  "version": "v1",
  "published": "2015-05-28T11:30:46.000Z",
  "updated": "2015-05-28T11:30:46.000Z",
  "title": "Graphs with small diameter determined by their $D$-spectra",
  "authors": [
    "Ruifang Liu",
    "Jie Xue"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph with vertex set $V(G)=\\{v_{1},v_{2},\\ldots,v_{n}\\}$. The distance matrix $D(G)=(d_{ij})_{n\\times n}$ is the matrix indexed by the vertices of $G,$ where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j}$. Suppose that $\\lambda_{1}(D)\\geq\\lambda_{2}(D)\\geq\\cdots\\geq\\lambda_{n}(D)$ are the distance spectrum of $G$. The graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph having the same spectrum as $G$ is isomorphic to $G$. In this paper, we give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their $D$-spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-28T11:30:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "small diameter",
      "distance matrix",
      "distance characteristic polynomial",
      "distance spectrum",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507651X"
    }
  }
}