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- Title
The Kirchhoff Index of Hypercubes and Related Complex Networks.
- Authors
Jiabao Liu; Jinde Cao; Xiang-Feng Pan; Elaiw, Ahmed
- Abstract
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.
- Subjects
KIRCHHOFF'S theory of diffraction; HYPERCUBES; MATHEMATICAL complexes; GRAPH theory; PATHS &; cycles in graph theory; POLYNOMIALS; LAPLACIAN matrices
- Publication
Discrete Dynamics in Nature & Society, 2013, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2013/543189