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Graph homomorphisms and nodal domains [electronic resource]
, Article Linear Algebra and its Applications ; 2006, Volume 418, Issue 1, Pages 44–52 ; Sharif University of Technology
Abstract
In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs
Graph homomorphisms and nodal domains
, Article Linear Algebra and Its Applications ; Volume 418, Issue 1 , 2006 , Pages 44-52 ; 00243795 (ISSN) ; Hajiabolhassan, H ; Sharif University of Technology
2006
Abstract
In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher's inequality for G-designs. © 2006 Elsevier Inc. All rights reserved
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes [electronic resource]
, Article Stochastic Processes and their Applications ; Volume 122, Issue 4, April 2012, Pages 1748–1776 ; Javadi, Ramin ; Miclo, Laurent ; Sharif Univercity of Technology
Abstract
Let LL be a reversible Markovian generator on a finite set View the MathML sourceV. Relations between the spectral decomposition of LL and subpartitions of the state space View the MathML sourceV into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle ZNZN, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as...
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
, Article Stochastic Processes and their Applications ; Volume 122, Issue 4 , April , 2012 , Pages 1748-1776 ; 03044149 (ISSN) ; Javadi, R ; Miclo, L ; Sharif University of Technology
2012
Abstract
Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min-max or max-min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle Z N, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum...