{
  "id": "1703.10460",
  "version": "v1",
  "published": "2017-03-30T13:26:38.000Z",
  "updated": "2017-03-30T13:26:38.000Z",
  "title": "On the spectrum of linear dependence graph of finite dimensional vector spaces",
  "authors": [
    "A. K. Bhuniya",
    "Sushobhan Maity"
  ],
  "comment": "3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we introduce a graph structure called linear dependence graph of a finite dimensional vector space over a finite field. Some basic properties of the graph like connectedness, completeness, planarity, clique number, chromatic number etc. have been studied. It is shown that two vector spaces are isomorphic if and only if their corresponding linear dependence graphs are isomorphic. Also adjacency spectrum, Laplacian spectrum and distance spectrum of the linear dependence graph have been studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T13:26:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C50",
      "05C69"
    ],
    "keywords": [
      "finite dimensional vector space",
      "corresponding linear dependence graphs",
      "graph structure",
      "adjacency spectrum",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}