{ "ok": true, "doi": "10.46243/jstj.2020.v5.i1.229", "doi_display": "10.46243/jstj.2020.v5.i1.229", "doi_url": "https://doi.org/10.46243/jstj.2020.v5.i1.229", "state": "registered", "url": "https://www.jst.org.in/index.php/pub/article/view/229", "title": "Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs", "version": 2, "registered_via": "crossref", "prefix": { "prefix": "10.46243", "status": "live" }, "registrant": { "name": "Longman Publishers", "kind": "publisher", "country": "India" }, "reserved_at": null, "registered_at": "2026-09-29 22:00:37", "updated_at": "2026-09-29 23:59:57", "withdrawn_at": null, "withdrawn_reason": null, "record": { "format": "smartscholars-doi-metadata/1.0", "doi": "10.46243/jstj.2020.v5.i1.229", "referent": "Creation", "type": "JournalArticle", "structural_type": "Digital", "modes": [ "Visual" ], "characters": [ "Language" ], "titles": [ { "value": "Geodetic Dominating Set and Geodetic Domination Polynomials of Extended Grid Graphs", "type": "PrincipalTitle", "lang": "en" } ], "identifiers": [ { "type": "DOI", "value": "10.46243/jstj.2020.v5.i1.229" } ], "agents": [ { "role": "author", "name": { "given": "N.Jaspin", "family": "Beaula" }, "sequence": "first" }, { "role": "author", "name": { "given": "Dr.A", "family": "Vijayan" }, "sequence": "additional" }, { "role": "publisher", "name": { "org": "Longman Publishers" } } ], "dates": { "published": "2020-01-02", "date_type": "PublicationDate", "online": "2020-01-02" }, "language": "en", "container": { "type": "Journal", "titles": [ { "value": "Journal of Science & Technology", "type": "PrincipalTitle" } ], "identifiers": [ { "type": "ISSN", "value": "2456-5660", "medium": "electronic" } ], "volume": "05", "issue": "01", "pages": { "first": "09", "last": "16" } }, "links": [ { "url": "https://www.jst.org.in/index.php/pub/article/view/229", "return_type": "text/html", "primary": true }, { "url": "https://www.jst.org.in/index.php/pub/article/download/229/201", "purpose": "text-mining", "return_type": "application/pdf" }, { "url": "https://www.jst.org.in/index.php/pub/article/download/229/2969", "purpose": "text-mining", "return_type": "application/xml" } ], "abstract": { "value": "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.", "lang": "en" }, "license": { "url": "https://creativecommons.org/licenses/by/4.0/", "start": "2020-01-02", "applies_to": "vor" }, "references": [ { "key": "ref1", "doi": "10.1155/2009/542040", "unstructured": "Alikhani. S and Peng. Y.H, \"Dominating Sets and Domination Polynomials of Paths\", International Journal of Mathematics and Mathematical Sciences, 10, 2009" }, { "key": "ref2", "unstructured": "Alikhani. S, Peng Y.H, \"Dominating sets and Domination Polynomial of Cycles\", Global Journal of Pure and Applied Mathematics 4 (2008) 2, 151–162" }, { "key": "ref3", "unstructured": "Alikhani. S, Peng. Y.H, \"Introduction to Domination Polynomial of a Graph\", Ars Combinatoria, Available as arXiv: 0905. 2251 v1 [math.CO] 14 May 2009" }, { "key": "ref4", "unstructured": "Chartand.G and Zhang. P, \"Introduction to Graph Theory\", McGraw-Hill, Boston, Mass, USA, 2005" }, { "key": "ref5", "unstructured": "A. Vijayan and S.Sanal Kumar, On Total Domination Sets and Polynomial of paths, International Journal of Mathematics Research, Vol.4(4), (2012), 339-348" }, { "key": "ref6", "doi": "10.4236/ojdm.2013.31013", "unstructured": "A. Vijayan, K. Lal Gipson, Dominating Sets and Domination Polynomials of square of paths, open Journal of Discrete Mathematics,Vol.3 (2013),60-69" }, { "key": "ref7", "doi": "10.9790/5728-0340414", "unstructured": "A. Vijayan, K. Lal Gipson, Dominating Sets and Domination Polynomials of square of cycles, IOSR Journal of Mathematics, Vol.3(4),(2012), 04-14" }, { "key": "ref8", "doi": "10.14445/22315373/ijmtt-v11p507", "unstructured": "A. Vijayan, T. Anitha Baby, Connected Total Dominating Sets and Connected Total Domination Polynomials of square of paths, International Journal of Mathematics Trends and Technology, Vol. 11,(1), 2014" }, { "key": "ref9", "doi": "10.14445/22315373/ijmtt-v11p507", "unstructured": "A.Vijayan, T. Anitha Baby, Connected Total Dominating Sets and Connected Total Domination Polynomials of Graphs, International Journal of Mathematics Achieve, Vol. 11,(1), 2014" }, { "key": "ref10", "unstructured": "T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamental of Domination in graphs, Vol. 208 of Monographs and Textbooks in Pure and Applied mathematics, Marcel Dekker, New York, NY, USA, 1998" } ], "record": { "registrant": "Longman Publishers", "registered": "2026-09-08", "updated": "2026-09-20", "issue_number": 1, "source": "crossref-api", "source_agency": "Crossref (member 25296)" } }, "record_sha256": "b4e05db45c8241a948842255c3e92ebbbf25880842992b013b894b5180c528d4", "handle": { "synced_at": "2026-10-01 18:13:35", "url": "https://www.jst.org.in/index.php/pub/article/view/229" }, "links": { "record_page": "https://registry.smartscholars.in/record.php?doi=10.46243%2Fjstj.2020.v5.i1.229", "system_metadata": "https://registry.smartscholars.in/resolve.php?doi=10.46243%2Fjstj.2020.v5.i1.229&as=system", "history": "https://registry.smartscholars.in/api.php?action=history&doi=10.46243%2Fjstj.2020.v5.i1.229", "kernel_xml": "https://registry.smartscholars.in/resolve.php?doi=10.46243%2Fjstj.2020.v5.i1.229&as=xml" } }