Please use this identifier to cite or link to this item:
Title: Combinatorial Perron values of trees and bottleneck matrices
Author: Andrade, Enide
Dahl, Geir
Keywords: Perron value
bottleneck matrix
Laplacian matrix
Issue Date: 2017
Publisher: Taylor & Francis
Abstract: The algebraic connectivity $a(G)$ of a graph $G$ is an important parameter, defined as the second smallest eigenvalue of the Laplacian matrix of $G$. If $T$ is a tree, $a(T)$ is closely related to the Perron values (spectral radius) of so-called bottleneck matrices of subtrees of $T$. In this setting we introduce a new parameter called the {\em combinatorial Perron value} $\rho_c$. This value is a lower bound on the Perron value of such subtrees; typically $\rho_c$ is a good approximation to $\rho$. We compute exact values of $\rho_c$ for certain special subtrees. Moreover, some results concerning $\rho_c$ when the tree is modified are established, and it is shown that, among trees with given distance vector (from the root), $\rho_c$ is maximized for caterpillars.
Peer review: yes
DOI: 10.1080/03081087.2016.1274363
ISSN: 0308-1087
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

Files in This Item:
File Description SizeFormat 
Combinatorial Perron values of trees and bottleneck matrices.pdf1.78 MBAdobe PDFrestrictedAccess

Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.