{
  "id": "1612.05505",
  "version": "v1",
  "published": "2016-12-15T04:02:31.000Z",
  "updated": "2016-12-15T04:02:31.000Z",
  "title": "Super-Walk Formulae for Even and Odd Laplacians in Finite Graphs",
  "authors": [
    "Chengzheng Yu"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The number of walks from one vertex to another in a finite graph can be counted by the adjacency matrix. In this paper, we prove two theorems that connect the graph Laplacian with two types of walks in a graph. By defining two types of walks and giving orientation to a finite graph, one can easily count the number of the total signs of each kind of walk from one element to another with a fixed length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-15T04:02:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite graph",
      "odd laplacians",
      "super-walk formulae",
      "adjacency matrix",
      "graph laplacian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}