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Titolo:
On a conjecture of Lewin's problem
Autore:
Liu, BL; Jiang, W;
Indirizzi:
S China Normal Univ, Dept Math, Guangzhou 510631, Peoples R China S China Normal Univ Guangzhou Peoples R China 510631 31, Peoples R China Guangdong Polytech Normal Univ, Dept Comp Sci, Guangzhou 510633, Peoples RChina Guangdong Polytech Normal Univ Guangzhou Peoples R China 510633 s RChina
Titolo Testata:
LINEAR ALGEBRA AND ITS APPLICATIONS
fascicolo: 1-3, volume: 323, anno: 2001,
pagine: 201 - 206
SICI:
0024-3795(20010115)323:1-3<201:OACOLP>2.0.ZU;2-2
Fonte:
ISI
Lingua:
ENG
Keywords:
Lewins's number; conjecture; exponent;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
5
Recensione:
Indirizzi per estratti:
Indirizzo: Liu, BL S China Normal Univ, Dept Math, Guangzhou 510631, Peoples R China S China Normal Univ Guangzhou Peoples R China 510631 les R China
Citazione:
B.L. Liu e W. Jiang, "On a conjecture of Lewin's problem", LIN ALG APP, 323(1-3), 2001, pp. 201-206

Abstract

Let digraph G be a primitive digraph. The parameter l(G) introduced by M. Lewin [Numer. Math. 18 (1971) 154] is the smallest positive integer k for which there are both a walk of length k and a walk of length k + 1 from somevertex u to some vertex v. As we know, the exponent of G is the smallest ksuch that there is a walk of length exactly k from each vertex u to each vertex v in G. J. Shen and S. Neufeld [Linear Algebra Appl. 274 (1998) 411] conjectured exp(G)/l(G) greater than or equal to 2 except G congruent to K-n* (complete graph with loop at each vertex). In this paper, the conjecturewas proved for undirected graph, and all primitive undirected graphs attaining this lower bound were characterized. (C) 2001 Published by Elsevier Science Inc, All rights reserved.

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Documento generato il 26/01/20 alle ore 01:20:34