{
  "id": "1304.3524",
  "version": "v1",
  "published": "2013-04-12T02:21:07.000Z",
  "updated": "2013-04-12T02:21:07.000Z",
  "title": "Characterization of tricyclic graphs with exactly two $Q$-main eigenvalues",
  "authors": [
    "Shuchao Li",
    "Xue Yang"
  ],
  "comment": "25 pages;6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The signless Laplacian matrix of a graph $G$ is defined to be the sum of its adjacency matrix and degree diagonal matrix, and its eigenvalues are called $Q$-eigenvalues of $G$. A $Q$-eigenvalue of a graph $G$ is called a $Q$-main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Chen and Huang [L. Chen, Q.X. Huang, Trees, unicyclic graphs and bicyclic graphs with exactly two $Q$-main eigenvalues, submitted for publication] characterized all trees, unicylic graphs and bicyclic graphs with exactly two main $Q$-eigenvalues, respectively. As a continuance of it, in this paper, all tricyclic graphs with exactly two $Q$-main eigenvalues are characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-12T02:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A18"
    ],
    "keywords": [
      "main eigenvalue",
      "tricyclic graphs",
      "characterization",
      "bicyclic graphs",
      "degree diagonal matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3524L"
    }
  }
}