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dc.contributor.authorFeng, Lihuaen_US
dc.contributor.authorLu, Luen_US
dc.contributor.authorStevanović, Draganen_US
dc.date.accessioned2020-12-09T09:08:51Z-
dc.date.available2020-12-09T09:08:51Z-
dc.date.issued2020-02-10-
dc.description.abstractFor a given graph, let wk denote the number of its walks with k vertices and let λ1 denote the spectral radius of its adjacency matrix. Nikiforov asked in [Linear Algebra Appl 418 (2006), 257–268] whether it is true in a connected bipartite graph that λr1≥ws+rws for every even s≥2 and even r≥2? We construct here several infinite sequences of connected bipartite graphs with two main eigenvalues for which the ratio ws+rλr1ws is larger than~1 for every even s,r≥2, and thus provide a negative answer to the above problem.en_US
dc.publisherPSR Pressen_US
dc.relationGraph theory and mathematical programming with applications in chemistry and computer scienceen_US
dc.relation.ispartofOpen Journal of Discrete Applied Mathematicsen_US
dc.subjectWalks in a graph | spectral radius | main eigenvaluesen_US
dc.titleWalk counting and Nikiforov’s problemen_US
dc.typeArticleen_US
dc.identifier.doi10.30538/psrp-odam2020.0024-
dc.identifier.urlhttps://pisrt.org/psrpress/j/odam/2020/1/3/walk-counting-and-nikiforov-s-problem.pdf-
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.grantno174033en_US
dc.relation.firstpage11-
dc.relation.lastpage19-
dc.relation.issue1-
dc.relation.volume3-
dc.description.rankM53-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
crisitem.author.orcid0000-0003-2908-305X-
crisitem.project.projectURLhttp://www.mi.sanu.ac.rs/novi_sajt/research/projects/174033e.php-
crisitem.project.fundingProgramDirectorate for Computer & Information Science & Engineering-
crisitem.project.openAireinfo:eu-repo/grantAgreement/NSF/Directorate for Computer & Information Science & Engineering/1740333-
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