Kirchhoff indexes of a network
type: Item
instance of: scholarly article
title: Kirchhoff indexes of a network
zbMATH Open document ID: 1195.94100
author: J. M. Gesto
author: Enrique Bendito
author: A. Carmona
author: A. M. Encinas
author: M. Mitjana
published in: Linear Algebra and its Applications
publication date: 2010-04-06T00:00:00Z
review text: A definition of the \textsl{effective resistance between any pair of vertices with respect to a value \(\lambda \geq 0\) and a weight \(w\)} on the vertex set of a network is developed, underlying the treatment of a generalization of the Kirchhoff index of a finite network. Connections are explored between the effective resistance and eigenvalues of the associated Schrödinger operator. Explicit expressions for effective resistances are derived, which enable the calculation of effective resistances and the generalized Kirchoff index for two sparse families of networks, ``wagon-wheels'' and ``circular ladders''.
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5689444
zbMATH Keywords: effective resistance
zbMATH Keywords: Kirchhoff index
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: Green function
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
full work available at URL: j.laa.2009.05.032
OpenAlex ID: W1972400840
cites work: Potential theory for Schrödinger operators on finite networks
cites work: Bounds on the first nonzero eigenvalue for self-adjoint boundary value problems on networks
cites work: The curl of a weighted network
cites work: Characterization of symmetric \(M\)-matrices as resistive inverses
cites work: Laplacian eigenvectors of graphs. Perron-Frobenius and Faber-Krahn type theorems
cites work: Resistance distance and the normalized Laplacian spectrum
cites work: Q5691133
cites work: A combinatorial Laplacian with vertex weights
cites work: Minimizing Effective Resistance of a Graph
cites work: Random walks and the effective resistance of networks
DOI: 10.1016/J.LAA.2009.05.032
description: scientific article; zbMATH DE number 5689444