{
  "id": "1704.05994",
  "version": "v1",
  "published": "2017-04-20T03:38:06.000Z",
  "updated": "2017-04-20T03:38:06.000Z",
  "title": "Edge Connectivity, Packing Spanning Trees, and eigenvalues of Graphs",
  "authors": [
    "Cunxiang Duan",
    "Ligong Wang",
    "Xiangxiang Liu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\tau(G)$ be the maximum number of edge-disjoint spanning trees of a graph $G$. A multigraph is a graph with possible multiple edges, but no loops. The multiplicity is the maximum number of edges between any pair of vertices. Motivated by a question of Seymour on the relationship between eigenvalues of a graph $G$ and bounds of $\\tau(G)$, we use adjacency quotient matrix and signless Laplacian quotient matrix to get the relationship between eigenvalues of a simple graph $G$ and bounds of $\\tau(G)$ and edge connectivity $\\kappa'(G)$. And we study the relationship between eigenvalues and bounds of $\\tau(G)$ and edge connectivity $\\kappa'(G)$ in a multigraph $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-20T03:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C40",
      "05C05"
    ],
    "keywords": [
      "edge connectivity",
      "packing spanning trees",
      "eigenvalues",
      "maximum number",
      "adjacency quotient matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}