On a graph of monogenic semigroups

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dc.contributor.authorDas, Kinkar Ch.
dc.contributor.authorAkgüneş, Nihat
dc.contributor.authorÇevik, A. Sinan
dc.date.accessioned2020-03-26T18:42:43Z
dc.date.available2020-03-26T18:42:43Z
dc.date.issued2013
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractLet us consider the finite monogenic semigroup S-M with zero having elements {x, x(2), x(3), ... , x(n)}. There exists an undirected graph Gamma (S-M) associated with S-M whose vertices are the non-zero elements x, x(2), x(3), ... , x(n) and, f or 1 <= i, j <= n, any two distinct vertices xi and xj are adjacent if i + j > n. In this paper, the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index and also perfectness of Gamma (S-M) have been established. In fact, some of the results obtained in this section are sharper and stricter than the results presented in DeMeyer et al. (Semigroup Forum 65:206-214, 2002). Moreover, the number of triangles for this special graph has been calculated. In the final part of the paper, by considering two (not necessarily different) graphs Gamma (S-M(1)) and Gamma (S-M(2)), we present the spectral properties to the Cartesian product Gamma (S-M(1)) square Gamma (S-M(2)).en_US
dc.description.sponsorshipFaculty Research Fund, Sungkyunkwan University; Sungkyunkwan University BK21 Project, BK21 Math Modelling HRD Div. Sungkyunkwan University, Suwon, Republic of Korea; Research Project Office of Selcuk UniversitySelcuk Universityen_US
dc.description.sponsorshipThe first author is supported by the Faculty Research Fund, Sungkyunkwan University, 2012 and Sungkyunkwan University BK21 Project, BK21 Math Modelling HRD Div. Sungkyunkwan University, Suwon, Republic of Korea. The second and third authors are both partially supported by the Research Project Office of Selcuk University. Some of the material in this paper can also be found in the second author's Ph.D. thesis.en_US
dc.identifier.doi10.1186/1029-242X-2013-44en_US
dc.identifier.issn1029-242Xen_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://dx.doi.org/10.1186/1029-242X-2013-44
dc.identifier.urihttps://hdl.handle.net/20.500.12395/29691
dc.identifier.wosWOS:000323562300004en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSPRINGER INTERNATIONAL PUBLISHING AGen_US
dc.relation.ispartofJOURNAL OF INEQUALITIES 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.subjectmonogenic semigroupen_US
dc.subjectzero-divisor graphen_US
dc.subjectclique numberen_US
dc.subjectchromatic numberen_US
dc.subjectindependence numberen_US
dc.subjectdomination numberen_US
dc.subjectnumber of trianglesen_US
dc.subjectCartesian producten_US
dc.titleOn a graph of monogenic semigroupsen_US
dc.typeArticleen_US

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