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The Kirchhoff Index of Hypercubes and Related Complex Networks
Joint Authors
Pan, Xiang-Feng
Liu, Jia-Bao
Cao, Jinde
Elaiw, A. M.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-12
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Liu, Jia-Bao& Cao, Jinde& Pan, Xiang-Feng& Elaiw, A. M.. 2013. The Kirchhoff Index of Hypercubes and Related Complex Networks. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-480184
Modern Language Association (MLA)
Liu, Jia-Bao…[et al.]. The Kirchhoff Index of Hypercubes and Related Complex Networks. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-480184
American Medical Association (AMA)
Liu, Jia-Bao& Cao, Jinde& Pan, Xiang-Feng& Elaiw, A. M.. The Kirchhoff Index of Hypercubes and Related Complex Networks. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-480184
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-480184