{
  "id": "1709.08871",
  "version": "v1",
  "published": "2017-09-26T07:56:04.000Z",
  "updated": "2017-09-26T07:56:04.000Z",
  "title": "Spectral radius of a star with one long arm",
  "authors": [
    "Hyunshik Shin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A tree is said to be starlike if exactly one vertex has degree greater than two. In this paper, we will study the spectral properties of $S(n,k \\cdot 1)$, that is, the starlike tree with $k$ branches of length 1 and one branch of length $n$. The largest eigenvalue $\\lambda_1$ of $S(n,k \\cdot 1)$ satisfies $\\sqrt{k+1} \\leq \\lambda_1 < k/\\sqrt{k-1}$. Moreover, the largest eigenvalue of $S(n,k \\cdot 1)$ is equal to the largest eigenvalue of $S(k \\cdot (n+1) )$, which is the starlike tree that has $k$ branches of length $n-1$. Using the spectral radii of $S(n,k \\cdot 1)$ we can show",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T07:56:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "spectral radius",
      "long arm",
      "largest eigenvalue",
      "starlike tree",
      "spectral properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}