The number of spanning trees of a graph

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dc.contributor.authorDas, Kinkar Chandra
dc.contributor.authorÇevik, Ahmet Sinan
dc.contributor.buuauthorCangül, İsmail Naci
dc.contributor.departmentUludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.tr_TR
dc.contributor.orcid0000-0002-0700-5774tr_TR
dc.contributor.orcid0000-0003-2576-160Xtr_TR
dc.contributor.researcheridJ-3505-2017tr_TR
dc.contributor.scopusid57189022403tr_TR
dc.date.accessioned2023-05-29T08:45:29Z
dc.date.available2023-05-29T08:45:29Z
dc.date.issued2013-08
dc.description.abstractLet G be a simple connected graph of order n, m edges, maximum degree Delta(1) and minimum degree delta. Li et al. (Appl. Math. Lett. 23: 286-290, 2010) gave an upper bound on number of spanning trees of a graph in terms of n, m, Delta(1) and delta: t(G) <= delta (2m-Delta(1)-delta-1/n-3)(n-3). The equality holds if and only if G congruent to K-1,K-n-1, G congruent to K-n, G congruent to K-1 boolean OR (K-1 boolean OR Kn-2) or G congruent to K-n - e, where e is any edge of K-n. Unfortunately, this upper bound is erroneous. In particular, we show that this upper bound is not true for complete graph K-n. In this paper we obtain some upper bounds on the number of spanning trees of graph G in terms of its structural parameters such as the number of vertices (n), the number of edges (m), maximum degree (Delta(1)), second maximum degree (Delta(2)), minimum degree (delta), independence number (alpha), clique number (omega). Moreover, we give the Nordhaus-Gaddum-type result for number of spanning trees.en_US
dc.description.sponsorshipFaculty research Fund, Sungkyunkwan Universityen_US
dc.description.sponsorshipKorean Government (2013R1A1A2009341)en_US
dc.description.sponsorshipSelçuk Üniversitesien_US
dc.description.sponsorshipGlaucoma Research Foundationen_US
dc.description.sponsorshipHong Kong Baptist Universityen_US
dc.identifier.citationDas, K. C. vd. (2013). “The number of spanning trees of a graph”. Journal of Inequalities and Applications, 2013.en_US
dc.identifier.issn1029-242X
dc.identifier.scopus2-s2.0-84894413510tr_TR
dc.identifier.urihttps://doi.org/10.1186/1029-242X-2013-395
dc.identifier.urihttps://doi.org/10.1186/1029-242X-2013-395
dc.identifier.urihttp://hdl.handle.net/11452/32849
dc.identifier.volume2013tr_TR
dc.identifier.wos000336908800001tr_TR
dc.indexed.scopusScopusen_US
dc.indexed.wosSCIEen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.bapUludağ Üniversitesitr_TR
dc.relation.collaborationYurt içitr_TR
dc.relation.collaborationYurt dışıtr_TR
dc.relation.journalJournal of Inequalities and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergitr_TR
dc.relation.tubitakTUBİTAKtr_TR
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMathematicsen_US
dc.subjectGraphen_US
dc.subjectSpanning treesen_US
dc.subjectIndependence numberen_US
dc.subjectClique numberen_US
dc.subjectFirst Zagreb indexen_US
dc.subjectMolecular-orbitalsen_US
dc.subjectZagreb indexesen_US
dc.subject.scopusSignless Laplacian; Eigenvalue; Signed Graphen_US
dc.subject.wosMathematics, applieden_US
dc.subject.wosMathematicsen_US
dc.titleThe number of spanning trees of a graphen_US
dc.typeArticle
dc.wos.quartileQ2en_US

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