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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Bibliographic Details
Published in:	Linear & multilinear algebra Vol. 65; no. 9; pp. 1823 - 1837
Main Authors:	Carmona, Ángeles, Mitjana, Margarida, Monsó, Enric
Format:	Journal Article Publication
Language:	English
Published:	Abingdon Taylor & Francis 02.09.2017 Taylor & Francis Ltd
Subjects:	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
Online Access:	Get full text
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Summary:	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.
Bibliography:	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