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dc.contributor.authorSaygi, Elif
dc.contributor.authorEgecioglu, Omor
dc.date.accessioned2019-12-17T09:09:24Z
dc.date.available2019-12-17T09:09:24Z
dc.date.issued2018
dc.identifier.issn1300-0098
dc.identifier.urihttps://doi.org/10.3906/mat-1605-2
dc.identifier.urihttp://hdl.handle.net/11655/20544
dc.description.abstractLucas and Fibonacci cubes are special subgraphs of the binary hypercubes that have been proposed as models of interconnection networks. Since these families are closely related to hypercubes, it is natural to consider the nature of the hypercubes they contain. Here we study a generalization of the enumerator polynomial of the hypercubes in Lucas cubes, which q-counts them by their distance to the all 0 vertex. Thus, our bivariate polynomials refine the count of the number of hypercubes of a given dimension in Lucas cubes and for q = 1 they specialize to the cube polynomials of KlavZar and Mollard. We obtain many properties of these polynomials as well as the q-cube polynomials of Fibonacci cubes themselves. These new properties include divisibility, positivity, and functional identities for both families.
dc.language.isoen
dc.publisherScientific Technical Research Council Turkey-Tubitak
dc.relation.isversionof10.3906/mat-1605-2
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectMathematics
dc.titleQ-Counting Hypercubes in Lucas Cubes
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.relation.journalTurkish Journal Of Mathematics
dc.contributor.departmentOrta Öğretim Fen ve Matematik Alanlar Eğitimi
dc.identifier.volume42
dc.identifier.issue1
dc.identifier.startpage190
dc.identifier.endpage203
dc.indexingWoS
dc.indexingScopus


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