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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 |
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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. 351-358 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 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 Identifier | http://hdl.handle.net/10722/48608 |
ISSN | 2020 Impact Factor: 0.87 2015 SCImago Journal Rankings: 1.000 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Siu, MK | en_HK |
dc.contributor.author | Zhang, ZF | en_HK |
dc.contributor.author | Zhou, SM | en_HK |
dc.date.accessioned | 2008-05-22T04:18:50Z | - |
dc.date.available | 2008-05-22T04:18:50Z | - |
dc.date.issued | 2002 | en_HK |
dc.identifier.citation | Discrete Mathematics, 2002, v. 259, p. 351-358 | en_HK |
dc.identifier.issn | 0012-365X | 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 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.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 Attribution-NonCommercial-NoDerivatives 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=0012-365X&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/S0012-365X(02)00541-1 | en_HK |
dc.identifier.scopus | eid_2-s2.0-33845750736 | - |
dc.identifier.isi | WOS:000180085900032 | - |
dc.identifier.issnl | 0012-365X | - |