Effective resistances and Kirchhoff index in subdivision networks

We define a subdivision network 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 ne...

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Veröffentlicht in:Linear & multilinear algebra Jg. 65; H. 9; S. 1823 - 1837
Hauptverfasser: Carmona, Ángeles, Mitjana, Margarida, Monsó, Enric
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 02.09.2017
Taylor & Francis Ltd
Schlagworte:
15 Linear and multilinear algebra; matrix theory
31 Potential theory
31C Other generalizations
34 Ordinary differential equations
34B Boundary value problems
Classificació AMS
Grafs, Teoria de
Graph theory
Green kernel
Kirchhoff Index
Matemàtiques i estadística
Resistance distance
Subdivision network
Àrees temàtiques de la UPC
ISSN:0308-1087, 1563-5139
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Zusammenfassung:We define a subdivision network 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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2016.1256945