New upper bounds on the spectral radius of unicyclic graphs

Author	dc.contributor.author	Rojo, Oscar
Admission date	dc.date.accessioned	2010-01-28T17:40:41Z
Available date	dc.date.available	2010-01-28T17:40:41Z
Publication date	dc.date.issued	2008-02-01
Cita de ítem	dc.identifier.citation	ELSEVIER SCIENCE INC	en_US
Identifier	dc.identifier.issn	0024-3795
Identifier	dc.identifier.uri	https://repositorio.uchile.cl/handle/2250/125278
Abstract	dc.description.abstract	G = (V (G),E(G)) be a unicyclic simple undirected graph with largest vertex degree . Let Cr be the unique cycle of G. The graph G − E(Cr ) is a forest of r rooted treesT1,T2, . . .,Tr with root vertices v1, v2, . . ., vr , respectively. Let k(G) = max 1 i r {max{dist(vi, u) : u ∈ V (Ti )}} + 1, where dist(v, u) is the distance from v to u. Let μ1(G) and λ1(G) be the spectral radius of the Laplacian matrix and adjacency matrix of G, respectively. We prove that μ1(G) < + 2 − 1 cos π 2k(G) + 1 , whenever > 2 and λ1(G) < 2 − 1 cos π 2k(G) + 1 , whenever 4 or whenever = 3 and k(G) 4. © 2007 Elsevier Inc. All rights reserved. AMS classification: 5C50; 15A48; 05C05	en_US
Patrocinador	dc.description.sponsorship	Work supported by Project Fondecyt 1070537, Chile.	en_US
Lenguage	dc.language.iso	en	en_US
Publisher	dc.publisher	LINEAR ALGEBRA AND ITS APPLICATIONS, Volume: 428, Issue: 4, Pages: 754-764, 2008	en_US
Keywords	dc.subject	Tree	en_US
Título	dc.title	New upper bounds on the spectral radius of unicyclic graphs	en_US
Document type	dc.type	Artículo de revista