{
  "id": "2003.08782",
  "version": "v1",
  "published": "2020-03-18T04:07:30.000Z",
  "updated": "2020-03-18T04:07:30.000Z",
  "title": "On the largest eigenvalue of a mixed graph with partial orientation",
  "authors": [
    "Bo-Jun Yuan",
    "Yi Wang",
    "Yi-Zheng Fan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph and let $T$ be a spanning tree of $G$. A partial orientation $\\sigma$ of $G$ respect to $T$ is an orientation of the edges of $G$ except those edges of $T$, the resulting graph associated with which is denoted by $G_T^\\sigma$. In this paper we prove that there exists a partial orientation $\\sigma$ of $G$ respect to $T$ such that the largest eigenvalue of the Hermitian adjacency matrix of $G_T^\\sigma$ is at most the largest absolute value of the roots of the matching polynomial of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T04:07:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "partial orientation",
      "largest eigenvalue",
      "mixed graph",
      "hermitian adjacency matrix",
      "largest absolute value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}