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The Kirchhoff Index of Hypercubes and Related Complex Networks

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  • Jiabao Liu
  • Jinde Cao
  • Xiang-Feng Pan
  • Ahmed Elaiw

Abstract

The resistance distance between any two vertices of is defined as the network effective resistance between them if each edge of is replaced by a unit resistor. The Kirchhoff index Kf( ) is the sum of resistance distances between all the pairs of vertices in . We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks and its three variant networks , , by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of , , and were proposed, respectively.

Suggested Citation

  • Jiabao Liu & Jinde Cao & Xiang-Feng Pan & Ahmed Elaiw, 2013. "The Kirchhoff Index of Hypercubes and Related Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, December.
    • Handle: RePEc:hin:jnddns:543189
    DOI: 10.1155/2013/543189
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    Cited by:

    1. Sardar, Muhammad Shoaib & Hua, Hongbo & Pan, Xiang-Feng & Raza, Hassan, 2020. "On the resistance diameter of hypercubes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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