{
  "id": "math/0609111",
  "version": "v1",
  "published": "2006-09-04T18:13:41.000Z",
  "updated": "2006-09-04T18:13:41.000Z",
  "title": "Revisiting two classical results on graph spectra",
  "authors": [
    "Vladimir Nikiforov"
  ],
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let mu(G) and mu_min(G) be the largest and smallest eigenvalues of the adjacency matricx of a graph G. We refine quantitatively the following two results on graph spectra. (i) if H is a proper subgraph of a connected graph G, then mu(G)>mu(H). (ii) if G is a connected nonbipartite graph, then mu(G)>-mu_min(G).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-04T18:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "graph spectra",
      "classical results",
      "revisiting",
      "connected nonbipartite graph",
      "proper subgraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9111N"
    }
  }
}