The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation

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dc.contributor.authorYilmaz, Fatih
dc.contributor.authorBozkurt, Durmus
dc.date.accessioned2020-03-26T18:31:32Z
dc.date.available2020-03-26T18:31:32Z
dc.date.issued2012
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractRecently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the (i, j) entry of A(m) (A is adjacency matrix) is equal to the number of walks of length m from vertex i to vertex j, we show that elements of mth positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.en_US
dc.description.sponsorshipSelcuk UniversitySelcuk Universityen_US
dc.description.sponsorshipThis research is supported by Selcuk University Research Project Coordinatorship (BAP).en_US
dc.identifier.doi10.1155/2012/423163en_US
dc.identifier.issn1110-757Xen_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.urihttps://dx.doi.org/10.1155/2012/423163
dc.identifier.urihttps://hdl.handle.net/20.500.12395/28471
dc.identifier.wosWOS:000307579300001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherHINDAWI PUBLISHING CORPORATIONen_US
dc.relation.ispartofJOURNAL OF APPLIED MATHEMATICSen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.titleThe Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representationen_US
dc.typeArticleen_US

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