{
  "id": "2409.00268",
  "version": "v1",
  "published": "2024-08-30T21:49:44.000Z",
  "updated": "2024-08-30T21:49:44.000Z",
  "title": "Uniform Shared Neighborhood Structures in Edge-Regular Graphs",
  "authors": [
    "Jared DeLeo"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A shared neighborhood structure (SNS) in a graph is a subgraph induced by the intersection of the open neighbor sets of two adjacent vertices. If a SNS is the same for all adjacent vertices in an edge-regular graph, call the SNS a uniform shared neighborhood structure (USNS). USNS-forbidden graphs (graphs which cannot be a USNS of an edge-regular graph) and USNS in graph products of edge-regular graphs are examined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-30T21:49:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "05C76"
    ],
    "keywords": [
      "uniform shared neighborhood structure",
      "edge-regular graph",
      "adjacent vertices",
      "open neighbor sets",
      "usns-forbidden graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}