{
  "id": "2411.00292",
  "version": "v1",
  "published": "2024-11-01T01:04:58.000Z",
  "updated": "2024-11-01T01:04:58.000Z",
  "title": "Inverse eigenvalue problem for Laplacian matrices of a graph",
  "authors": [
    "Shaun Fallat",
    "Himanshu Gupta",
    "Jephian C. -H. Lin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This specialized inverse eigenvalue problem is considered for certain families of graphs and graphs on a small number of vertices. Related considerations include studying the possible ordered multiplicity lists associated with stars and complete graphs and graphs with a few vertices. Finally, we investigate the both theoretically and numerically, the minimum variance over a family of generalized Laplacian matrices with a size-normalized weighting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-01T01:04:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A18",
      "15B57",
      "65F18"
    ],
    "keywords": [
      "laplacian matrix",
      "specialized inverse eigenvalue problem",
      "ordered multiplicity lists",
      "generalized laplacian matrices",
      "minimum variance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}