The Kirchhoff Index of Some Combinatorial Networks

Jia-Bao Liu, Xiang-Feng Pan, Jinde Cao and Fu-Tao Hu

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-6

Abstract:

The Kirchhoff index Kf( ) is the sum of the effective resistance distances between all pairs of vertices in . The hypercube and the folded hypercube are well known networks due to their perfect properties. The graph , constructed from , is the line graph of the subdivision graph . In this paper, explicit formulae expressing the Kirchhoff index of and are found by deducing the characteristic polynomial of the Laplacian matrix of in terms of that of .

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:340793

DOI: 10.1155/2015/340793

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