The Kirchhoff Index of Some Combinatorial Networks
The Kirchhoff index Kf(G) is the sum of the effective resistance distances between all pairs of vertices in G. The hypercube Qn and the folded hypercube FQn are well known networks due to their perfect properties. The graph G∗, constructed from G, is the line graph of the subdivision graph S(G). In...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/340793 |
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| Summary: | The Kirchhoff index Kf(G) is the sum of the effective resistance distances between all pairs of vertices in G. The hypercube Qn and the folded hypercube FQn are well known networks due to their perfect properties. The graph G∗, constructed from G, is the line graph of the subdivision graph S(G). In this paper, explicit formulae expressing the Kirchhoff index of (Qn)∗ and (FQn)∗ are found by deducing the characteristic polynomial of the Laplacian matrix of G∗ in terms of that of G. |
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| ISSN: | 1026-0226 1607-887X |