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Effective resistances and Kirchhoff index in subdivision networks
Carmona Mejías, Ángeles; Mitjana Riera, Margarida; Monsó Burgués, Enrique P.J.
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes
We define a subdivision network ¿S of a given network ¿; by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a wheel.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística
Graph theory
Resistance distance
Green kernel
Kirchhoff Index
Subdivision network
Grafs, Teoria de
Classificació AMS::31 Potential theory::31C Other generalizations
Classificació AMS::15 Linear and multilinear algebra; matrix theory
Classificació AMS::34 Ordinary differential equations::34B Boundary value problems
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/submittedVersion
Article
Taylor & Francis
         

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