{
  "id": "1305.4317",
  "version": "v1",
  "published": "2013-05-19T01:50:42.000Z",
  "updated": "2013-05-19T01:50:42.000Z",
  "title": "The least eigenvalue of graphs whose complements are unicyclic",
  "authors": [
    "Yi Wang",
    "Yi-Zheng Fan",
    "Xiao-Xin Li",
    "Fei-Fei Zhang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph in a certain graph class is called minimizing if the least eigenvalue of the adjacency matrix of the graph attains the minimum among all graphs in that class. Bell {\\it et al.} have characterized the minimizing graphs in the class of connected graphs of order $n$ and size $m$, whose complements are either disconnected or contain a clique of order at least $n/2$. In this paper we discuss the minimizing graphs of a special class of graphs of order $n$ whose complements are connected and contains exactly one cycle (namely the the class $\\mathscr {U}^{c}_{n}$ of graphs whose complements are unicyclic), and characterize the unique minimizing graph in $\\mathscr {U}^{c}_{n}$ when $n \\geq 20$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-19T01:50:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05D05",
      "15A18"
    ],
    "keywords": [
      "complements",
      "eigenvalue",
      "adjacency matrix",
      "unique minimizing graph",
      "graph attains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4317W"
    }
  }
}