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Article: An inequality between the diameter and the inverse dual degree of a tree

TitleAn inequality between the diameter and the inverse dual degree of a tree
Authors
Siu, MKZhang, ZFZhou, SM
KeywordsTree
Diameter
Radius
Inverse dual degree
Graffiti conjecture
Issue Date2002
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/disc
Citation
Discrete Mathematics, 2002, v. 259, p. 351-358 How to Cite?
DOI: http://dx.doi.org/10.1016/S0012-365X(02)00541-1
AbstractLet T be a nontrivial tree with diameter D(T) and radius R(T). Let I(T) be the inverse dual degree of T which is defined to be , where for uV(T). For any longest path P of T, denote by a(P) the number of vertices outside P with degree at least 2, b(P) the number of vertices on P with degree at least 3 and distance at least 2 to each of the end-vertices of P, and c(P) the number of vertices adjacent to one of the end-vertices of P and with degree at least 3. In this note we prove that . As a corollary we then get with equality if and only if T is a path of at least four vertices. The latter inequality strengthens a conjecture made by the program Graffiti.
Persistent Identifierhttp://hdl.handle.net/10722/48608
ISSN
0012-365X
2023 Impact Factor: 0.7
2023 SCImago Journal Rankings: 0.801
ISI Accession Number ID
WOS:000180085900032

 

DC FieldValueLanguage
dc.contributor.authorSiu, MKen_HK
dc.contributor.authorZhang, ZFen_HK
dc.contributor.authorZhou, SMen_HK
dc.date.accessioned2008-05-22T04:18:50Z-
dc.date.available2008-05-22T04:18:50Z-
dc.date.issued2002en_HK
dc.identifier.citationDiscrete Mathematics, 2002, v. 259, p. 351-358en_HK
dc.identifier.issn0012-365Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/48608-
dc.description.abstractLet T be a nontrivial tree with diameter D(T) and radius R(T). Let I(T) be the inverse dual degree of T which is defined to be , where for uV(T). For any longest path P of T, denote by a(P) the number of vertices outside P with degree at least 2, b(P) the number of vertices on P with degree at least 3 and distance at least 2 to each of the end-vertices of P, and c(P) the number of vertices adjacent to one of the end-vertices of P and with degree at least 3. In this note we prove that . As a corollary we then get with equality if and only if T is a path of at least four vertices. The latter inequality strengthens a conjecture made by the program Graffiti.en_HK
dc.format.extent134915 bytes-
dc.format.extent545283 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/pdf-
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/discen_HK
dc.rightsDiscrete Mathematics. Copyright © Elsevier BV.en_HK
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectTreeen_HK
dc.subjectDiameteren_HK
dc.subjectRadiusen_HK
dc.subjectInverse dual degreeen_HK
dc.subjectGraffiti conjectureen_HK
dc.titleAn inequality between the diameter and the inverse dual degree of a treeen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0012-365X&volume=259&spage=351&epage=358&date=2002&atitle=+An+inequality+between+the+diameter+and+the+inverse+dual+degree+of+a+treeen_HK
dc.identifier.emailSiu, MK: mathsiu@hkucc.hku.hken_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1016/S0012-365X(02)00541-1en_HK
dc.identifier.scopuseid_2-s2.0-33845750736-
dc.identifier.isiWOS:000180085900032-
dc.identifier.issnl0012-365X-

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