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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| Format: | Article |
| Language: | English |
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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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| author | Jia-Bao Liu Xiang-Feng Pan Jinde Cao Fu-Tao Hu |
| author_facet | Jia-Bao Liu Xiang-Feng Pan Jinde Cao Fu-Tao Hu |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b1343a9bed8f4b20a56a9b643eef4de1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b1343a9bed8f4b20a56a9b643eef4de12025-02-03T06:01:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/340793340793The Kirchhoff Index of Some Combinatorial NetworksJia-Bao Liu0Xiang-Feng Pan1Jinde Cao2Fu-Tao Hu3Department of Public Courses, Anhui Xinhua University, Hefei 230088, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230601, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230601, ChinaThe 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.http://dx.doi.org/10.1155/2015/340793 |
| spellingShingle | Jia-Bao Liu Xiang-Feng Pan Jinde Cao Fu-Tao Hu The Kirchhoff Index of Some Combinatorial Networks Discrete Dynamics in Nature and Society |
| title | The Kirchhoff Index of Some Combinatorial Networks |
| title_full | The Kirchhoff Index of Some Combinatorial Networks |
| title_fullStr | The Kirchhoff Index of Some Combinatorial Networks |
| title_full_unstemmed | The Kirchhoff Index of Some Combinatorial Networks |
| title_short | The Kirchhoff Index of Some Combinatorial Networks |
| title_sort | kirchhoff index of some combinatorial networks |
| url | http://dx.doi.org/10.1155/2015/340793 |
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