Cite this DOI

Beaula, N., & Vijayan, D. (2020). Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs. *Journal of Science & Technology*, *05*(01), 09–16. https://doi.org/10.46243/jstj.2020.v5.i1.229

@article{beaula2020geodetic,
  author    = {Beaula, N.Jaspin and Vijayan, Dr.A},
  title     = {{Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs}},
  journal   = {Journal of Science \& Technology},
  year      = {2020},
  month     = {jan},
  volume    = {05},
  number    = {01},
  pages     = {09--16},
  publisher = {Longman Publishers},
  issn      = {2456-5660},
  doi       = {10.46243/jstj.2020.v5.i1.229},
  url       = {https://doi.org/10.46243/jstj.2020.v5.i1.229},
  language  = {en},
  abstract  = {Let G = (V,E) be a simple graph. A set S  V is a dominating set of G, if every vertex in V− S is adjacent to atleast one vertex S. Let Dg(Gn, i) be the family of geodetic dominating sets of the graph Gn with cardinality 'i'. Let dg(Gn, i) = | Dg(Gn, i)|. In this paper, we obtain a recursive for dg(Gn, i). Using the recursive formula, we construct the polynomial, g(Gn) = n + 1 2     , g(Gn − \{2n\}) = n + 1 2     which we call geodetic dominating polynomial of Gn and obtain some properties of this polynomial.}
}

TY  - JOUR
TI  - Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs
AU  - Beaula, N.Jaspin
AU  - Vijayan, Dr.A
JO  - Journal of Science & Technology
PY  - 2020
DA  - 2020/01/02/
VL  - 05
IS  - 01
SP  - 09
EP  - 16
PB  - Longman Publishers
SN  - 2456-5660
LA  - en
AB  - Let G = (V,E) be a simple graph. A set S  V is a dominating set of G, if every vertex in V− S is adjacent to atleast one vertex S. Let Dg(Gn, i) be the family of geodetic dominating sets of the graph Gn with cardinality 'i'. Let dg(Gn, i) = | Dg(Gn, i)|. In this paper, we obtain a recursive for dg(Gn, i). Using the recursive formula, we construct the polynomial, g(Gn) = n + 1 2     , g(Gn − {2n}) = n + 1 2     which we call geodetic dominating polynomial of Gn and obtain some properties of this polynomial.
DO  - 10.46243/jstj.2020.v5.i1.229
UR  - https://doi.org/10.46243/jstj.2020.v5.i1.229
ER  -

{
    "type": "article-journal",
    "id": "10.46243/jstj.2020.v5.i1.229",
    "DOI": "10.46243/jstj.2020.v5.i1.229",
    "URL": "https://doi.org/10.46243/jstj.2020.v5.i1.229",
    "title": "Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs",
    "source": "Smart Scholars DOI Registry",
    "container-title": "Journal of Science & Technology",
    "author": [
        {
            "family": "Beaula",
            "given": "N.Jaspin"
        },
        {
            "family": "Vijayan",
            "given": "Dr.A"
        }
    ],
    "issued": {
        "date-parts": [
            [
                2020,
                1,
                2
            ]
        ]
    },
    "volume": "05",
    "issue": "01",
    "page": "09-16",
    "publisher": "Longman Publishers",
    "language": "en",
    "abstract": "Let G = (V,E) be a simple graph. A set S  V is a dominating set of G, if every vertex in V− S is adjacent to atleast one vertex S. Let Dg(Gn, i) be the family of geodetic dominating sets of the graph Gn with cardinality 'i'. Let dg(Gn, i) = | Dg(Gn, i)|. In this paper, we obtain a recursive for dg(Gn, i). Using the recursive formula, we construct the polynomial, g(Gn) = n + 1 2     , g(Gn − {2n}) = n + 1 2     which we call geodetic dominating polynomial of Gn and obtain some properties of this polynomial.",
    "ISSN": "2456-5660"
}

From the record as registered (version 2) — the record and its history. Programs: https://registry.smartscholars.in/api.php?action=cite&doi=10.46243%2Fjstj.2020.v5.i1.229 gives all four in one JSON answer.