{
  "id": "2012.04020",
  "version": "v1",
  "published": "2020-12-07T19:53:14.000Z",
  "updated": "2020-12-07T19:53:14.000Z",
  "title": "$λ$-Core Distance Partitions",
  "authors": [
    "Xandru Mifsud"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $\\lambda$-core vertices of a graph correspond to the non-zero entries of some eigenvector of $\\lambda$ for a universal adjacency matrix $\\mathbf{U}$ of the graph. We define a partition of the vertex set $V$ based on the $\\lambda$-core vertex set and its neighbourhoods at a distance $r$, and give a number of results relating the structure of the graph to this partition. For such partitions, we also define an entropic measure for the information content of a graph, related to every distinct eigenvalue $\\lambda$ of $\\mathbf{U}$, and discuss its properties and potential applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-07T19:53:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A18"
    ],
    "keywords": [
      "core distance partitions",
      "universal adjacency matrix",
      "core vertex set",
      "non-zero entries",
      "graph correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}