{
  "id": "1610.03972",
  "version": "v1",
  "published": "2016-10-13T08:19:45.000Z",
  "updated": "2016-10-13T08:19:45.000Z",
  "title": "1-well-covered graphs revisited",
  "authors": [
    "Vadim E. Levit",
    "Eugen Mandrescu"
  ],
  "comment": "16 pages; 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A graph is well-covered if all its maximal independent sets are of the same size (M. D. Plummer, 1970). A well-covered graph (with at least two vertices) is 1-well-covered if the deletion of every vertex leaves a graph which is well-covered as well (J. W. Staples, 1975). In this paper, we provide new characterizations of 1-well-covered graphs, which we further use to build 1-well-covered graphs by corona, join, and concatenation operations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T08:19:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C75",
      "05C76",
      "05C25",
      "G.2.2"
    ],
    "keywords": [
      "maximal independent sets",
      "vertex leaves",
      "concatenation operations",
      "well-covered graph",
      "characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}