The Kirchhoff Index of Hypercubes and Related Complex Networks
The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formul...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/543189 |
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| author | Jiabao Liu Jinde Cao Xiang-Feng Pan Ahmed Elaiw |
| author_facet | Jiabao Liu Jinde Cao Xiang-Feng Pan Ahmed Elaiw |
| author_sort | Jiabao Liu |
| collection | DOAJ |
| description | The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Qn by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks Qn and its three variant networks l(Qn), s(Qn), t(Qn) by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of l(Qn), s(Qn), and t(Qn) were proposed, respectively. |
| format | Article |
| id | doaj-art-f4813454bf77450bb44671c88559ec53 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f4813454bf77450bb44671c88559ec532025-02-03T01:20:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/543189543189The Kirchhoff Index of Hypercubes and Related Complex NetworksJiabao Liu0Jinde Cao1Xiang-Feng Pan2Ahmed Elaiw3Department of Mathematics, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230601, ChinaDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi ArabiaThe resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Qn by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks Qn and its three variant networks l(Qn), s(Qn), t(Qn) by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of l(Qn), s(Qn), and t(Qn) were proposed, respectively.http://dx.doi.org/10.1155/2013/543189 |
| spellingShingle | Jiabao Liu Jinde Cao Xiang-Feng Pan Ahmed Elaiw The Kirchhoff Index of Hypercubes and Related Complex Networks Discrete Dynamics in Nature and Society |
| title | The Kirchhoff Index of Hypercubes and Related Complex Networks |
| title_full | The Kirchhoff Index of Hypercubes and Related Complex Networks |
| title_fullStr | The Kirchhoff Index of Hypercubes and Related Complex Networks |
| title_full_unstemmed | The Kirchhoff Index of Hypercubes and Related Complex Networks |
| title_short | The Kirchhoff Index of Hypercubes and Related Complex Networks |
| title_sort | kirchhoff index of hypercubes and related complex networks |
| url | http://dx.doi.org/10.1155/2013/543189 |
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