The graph based on Grobner-Shirshov bases of groups

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dc.contributor.authorKarpuz, Eylem G.
dc.contributor.authorAtes, Firat
dc.contributor.authorCevik, A. Sinan
dc.contributor.authorCangul, I. Naci
dc.date.accessioned2020-03-26T18:44:02Z
dc.date.available2020-03-26T18:44:02Z
dc.date.issued2013
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractLet us consider groups G(1) = Z(k) * (Z(m) * Z(n)), G(2) = Z(k) x (Z(m) * Z(n)), G(3) = Z(k) * (Z(m) x Z(n)), G(4) = (Z(k) * Z(l)) * (Z(m) * Z(n)) and G(5) = (Z(k) * Z(l)) x (Z(m) * Z(n)), where k, l, m, n = 2. In this paper, by defining a new graph Gamma(G(i)) based on the Grobner-Shirshov bases over groups G(i), where 1 <= i <= 5, we calculate the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of Gamma(G(i)). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in such fields as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics. In addition, the Grobner-Shirshov basis and the presentations of algebraic structures contain a mixture of algebra, topology and geometry within the purposes of this journal.en_US
dc.description.sponsorshipResearch Project Offices (BAP) of their universities in Turkeyen_US
dc.description.sponsorshipAll authors are partially supported by Research Project Offices (BAP) of their universities in Turkey.en_US
dc.identifier.doi10.1186/1687-1812-2013-71en_US
dc.identifier.issn1687-1812en_US
dc.identifier.urihttps://dx.doi.org/10.1186/1687-1812-2013-71
dc.identifier.urihttps://hdl.handle.net/20.500.12395/29932
dc.identifier.wosWOS:000326449400001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherSPRINGER INTERNATIONAL PUBLISHING AGen_US
dc.relation.ispartofFIXED POINT THEORY AND APPLICATIONSen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.subjectgraphsen_US
dc.subjectGrobner-Shirshov basesen_US
dc.subjectgroup presentationen_US
dc.titleThe graph based on Grobner-Shirshov bases of groupsen_US
dc.typeArticleen_US

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