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

Authors  
Keywords  Tree Diameter Radius Inverse dual degree Graffiti conjecture 
Issue Date  2002 
Publisher  Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/disc 
Citation  Discrete Mathematics, 2002, v. 259, p. 351358 How to Cite? 
Abstract  Let 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 endvertices of P, and c(P) the number of vertices adjacent to one of the endvertices 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 Identifier  http://hdl.handle.net/10722/48608 
ISSN  2015 Impact Factor: 0.6 2015 SCImago Journal Rankings: 1.000 
ISI Accession Number ID 
DC Field  Value  Language 

dc.contributor.author  Siu, MK  en_HK 
dc.contributor.author  Zhang, ZF  en_HK 
dc.contributor.author  Zhou, SM  en_HK 
dc.date.accessioned  20080522T04:18:50Z   
dc.date.available  20080522T04:18:50Z   
dc.date.issued  2002  en_HK 
dc.identifier.citation  Discrete Mathematics, 2002, v. 259, p. 351358  en_HK 
dc.identifier.issn  0012365X  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/48608   
dc.description.abstract  Let 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 endvertices of P, and c(P) the number of vertices adjacent to one of the endvertices 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.extent  134915 bytes   
dc.format.extent  545283 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  application/pdf   
dc.language  eng  en_HK 
dc.publisher  Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/disc  en_HK 
dc.rights  Discrete Mathematics. Copyright © Elsevier BV.  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject  Tree  en_HK 
dc.subject  Diameter  en_HK 
dc.subject  Radius  en_HK 
dc.subject  Inverse dual degree  en_HK 
dc.subject  Graffiti conjecture  en_HK 
dc.title  An inequality between the diameter and the inverse dual degree of a tree  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0012365X&volume=259&spage=351&epage=358&date=2002&atitle=+An+inequality+between+the+diameter+and+the+inverse+dual+degree+of+a+tree  en_HK 
dc.identifier.email  Siu, MK: mathsiu@hkucc.hku.hk  en_HK 
dc.description.nature  postprint  en_HK 
dc.identifier.doi  10.1016/S0012365X(02)005411  en_HK 
dc.identifier.isi  WOS:000180085900032   