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dc.contributor.authorBendito Pérez, Enrique
dc.contributor.authorCarmona Mejías, Ángeles
dc.contributor.authorEncinas Bachiller, Andrés Marcos
dc.contributor.authorGesto Beiroa, José Manuel
dc.contributor.authorMitjana Riera, Margarida
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.identifier.citationBendito, E. [et al.]. Kirchhoff indexes of a network. "Linear algebra and its applications", 15 Abril 2010, vol. 432, núm. 9, p. 2278-2292.
dc.description.abstractIn this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with symmetries, specifically for weighted wagon-wheels and circular ladders.
dc.format.extent15 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
dc.subject.lcshSchrödinger operators
dc.subject.lcshGreen's functions
dc.subject.lcshAlgebras, Linear
dc.subject.lcshLambda algebra
dc.titleKirchhoff indexes of a network
dc.subject.lemacGreen, Funcions de
dc.subject.lemacÀlgebra lineal
dc.subject.lemacSchrödinger, Equació de
dc.contributor.groupUniversitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
upcommons.citation.authorBendito, E.; Carmona, Á.; Encinas, A.; Gesto, J.; Mitjana, M.
upcommons.citation.publicationNameLinear algebra and its applications

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