{
  "id": "1910.12110",
  "version": "v1",
  "published": "2019-10-26T17:51:25.000Z",
  "updated": "2019-10-26T17:51:25.000Z",
  "title": "A Characterization For 2-Self-Centered Graphs",
  "authors": [
    "Mohammad Hadi Shekarriz",
    "Madjid Mirzavaziri",
    "Kamyar Mirzavaziri"
  ],
  "journal": "Discussiones Mathematicae Graph Theory 38 (2018) 27-37",
  "doi": "10.7151/dmgt.1994",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing \\emph{specialized bi-independent covering (SBIC)} and a structure named \\emph{generalized complete bipartite graph (GCBG)}. Then, we complete characterization by characterizing edge-minimal 2-self-centered graphs with some triangles. Hence, the main characterization is done since a graph is 2-self-centered if and only if it is a spanning subgraph of some edge-maximal 2-self-centered graphs and, at the same time, it is a spanning supergraph of some edge-minimal 2-self-centered graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-26T17:51:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C69"
    ],
    "keywords": [
      "complete bipartite graph",
      "main characterization",
      "complete characterization",
      "split characterizing edge-minimal",
      "characterize edge-minimal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}