{
  "id": "1409.6065",
  "version": "v1",
  "published": "2014-09-22T01:58:49.000Z",
  "updated": "2014-09-22T01:58:49.000Z",
  "title": "Edge-connectivity in regular multigraphs from eigenvalues",
  "authors": [
    "Suil O"
  ],
  "comment": "11 pages, 2 figures (in press, Linear Algebra and its Application)",
  "doi": "10.1016/j.laa.2014.09.015",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a $d$-regular multigraph, and let $\\lambda_2(G)$ be the second largest eigenvalue of $G$. In this paper, we prove that if $\\lambda_2(G) < \\frac{d-1+\\sqrt{9d^2-10d+17}}4$, then $G$ is 2-edge-connected. Furthermore, for $t\\ge2$ we show that $G$ is $(t+1)$-edge-connected when $\\lambda_2(G)<d-t$, and in fact when $\\lambda_2(G)<d-t+1$ if $t$ is odd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-22T01:58:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C40"
    ],
    "keywords": [
      "regular multigraph",
      "edge-connectivity",
      "second largest eigenvalue"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6065O"
    }
  }
}