The Kirchhoff Index of Hypercubes and Related Complex Networks
| Autor: | Jiabao Liu, Jinde Cao, Xiang-Feng Pan, Ahmed Elaiw |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2013 (2013) |
| Druh dokumentu: | article |
| ISSN: | 1026-0226 1607-887X |
| DOI: | 10.1155/2013/543189 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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