On the spectral radius of bipartite graphs which are nearly complete

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dc.contributor.authorDas, Kinkar Chandra
dc.contributor.authorCangul, Ismail Naci
dc.contributor.authorMaden, Ayse Dilek
dc.contributor.authorCevik, Ahmet Sinan
dc.date.accessioned2020-03-26T18:42:46Z
dc.date.available2020-03-26T18:42:46Z
dc.date.issued2013
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractFor p, q, r, s, t is an element of Z(+) with rt <= p and st <= q, let G = G(p, q; r, s; t) be the bipartite graph with partite sets U = {u(1), ..., u(p)} and V = {v(1),..., v(q)} such that any two edges u(i) and v(j) are not adjacent if and only if there exists a positive integer k with 1 <= k <= t such that (k - 1) r + 1 <= i <= kr and (k - 1) s + 1 <= j <= ks. Under these circumstances, Chen et al. (Linear Algebra Appl. 432: 606-614, 2010) presented the following conjecture: Assume that p <= q, k < p, vertical bar U vertical bar = p, vertical bar V vertical bar = q and vertical bar E(G)vertical bar = pq - k. Then whether it is true that lambda(1)(G) <= lambda(1)(G(p, q; k, 1; 1)) = root pq - k + root p(2)q(2) - 6pqk + 4pk + 4qk(2) - 3k(2)/2. In this paper, we prove this conjecture for the range min(vh is an element of V){deg v(h)} <= left perpendicular p-1/2right perpendicular.en_US
dc.description.sponsorshipBK21 Math Modeling HRD Div. Sungkyunkwan University, Suwon, Republic of KoreaMinistry of Education & Human Resources Development (MOEHRD), Republic of Korea; Research Project Offices of UludagUludag University; Selcuk UniversitiesSelcuk Universityen_US
dc.description.sponsorshipThe first author is supported by BK21 Math Modeling HRD Div. Sungkyunkwan University, Suwon, Republic of Korea, and the other authors are partially supported by Research Project Offices of Uludag (2012-15 and 2012-19) and Selcuk Universities.en_US
dc.identifier.doi10.1186/1029-242X-2013-121en_US
dc.identifier.issn1029-242Xen_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://dx.doi.org/10.1186/1029-242X-2013-121
dc.identifier.urihttps://hdl.handle.net/20.500.12395/29704
dc.identifier.wosWOS:000317992400001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSPRINGEROPENen_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.subjectbipartite graphen_US
dc.subjectadjacency matrixen_US
dc.subjectspectral radiusen_US
dc.titleOn the spectral radius of bipartite graphs which are nearly completeen_US
dc.typeArticleen_US

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