The Kirchhoff index of some combinatorial networks
type: Item
instance of: scholarly article
title: The Kirchhoff index of some combinatorial networks
zbMATH Open document ID: 1418.05116
DOI: 10.1155/2015/340793
author: Jiabao Liu
author: Xiang-Feng Pan
author: Fu-Tao Hu
author: Jinde Cao
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: The Kirchhoff index Kf(\(G\)) is the sum of the effective resistance distances between all pairs of vertices in \(G\). The hypercube \(Q_n\) and the folded hypercube \(F Q_n\) are well known networks due to their perfect properties. The graph \(G^{\ast}\), constructed from \(G\), is the line graph of the subdivision graph \(S(G)\). In this paper, explicit formulae expressing the Kirchhoff index of \((Q_n)^{\ast}\) and \((F Q_n)^{\ast}\) are found by deducing the characteristic polynomial of the Laplacian matrix of \(G^{\ast}\) in terms of that of \(G\).
Mathematics Subject Classification ID: 05C82
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 7025321
Wikidata QID: Q59105828
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/340793
OpenAlex ID: W1891707693
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description: scientific article; zbMATH DE number 7025321