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  • 标题:The Kirchhoff Index of Hypercubes and Related Complex Networks
  • 本地全文:下载
  • 作者:Jiabao Liu ; Jinde Cao ; Xiang-Feng Pan
  • 期刊名称:Discrete Dynamics in Nature and Society
  • 印刷版ISSN:1026-0226
  • 电子版ISSN:1607-887X
  • 出版年度:2013
  • 卷号:2013
  • 页码:1-7
  • DOI:10.1155/2013/543189
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    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 Q n by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks Q n and its three variant networks l ( Q n ) , s ( Q n ) , t ( Q n ) by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of l ( Q n ) , s ( Q n ) , and t ( Q n ) were proposed, respectively.

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