{
  "id": "math/9912234",
  "version": "v1",
  "published": "1999-12-30T20:18:33.000Z",
  "updated": "1999-12-30T20:18:33.000Z",
  "title": "On $α$-Square-Stable Graphs",
  "authors": [
    "Vadim E. Levit",
    "Eugen Mandrescu"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G) + mu(G) equals its order, then G is a Koenig-Egervary graph. We call G an $\\alpha $-square-stable graph, shortly square-stable, if alpha(G) = alpha(G*G), where G*G denotes the second power of G. These graphs were first investigated by Randerath and Wolkmann. In this paper we obtain several new characterizations of square-stable graphs. We also show that G is an square-stable Koenig-Egervary graph if and only if it has a perfect matching consisting of pendant edges. Moreover, we find that well-covered trees are exactly square-stable trees. To verify this result we give a new proof of one Ravindra's theorem describing well-covered trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-30T20:18:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "05C69",
      "05C05",
      "05C70"
    ],
    "keywords": [
      "square-stable graph",
      "ravindras theorem describing well-covered trees",
      "pendant edges",
      "cardinality",
      "second power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12234L"
    }
  }
}