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Mathematical Problems in Engineering
Volume 2014, Article ID 380874, 9 pages
Research Article

The Kirchhoff Index of Folded Hypercubes and Some Variant Networks

1School of Mathematics Science, Anhui University, Hefei 230601, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Anhui Xinhua University, Hefei 230088, China
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 3 November 2013; Accepted 25 November 2013; Published 16 January 2014

Academic Editor: Chuangxia Huang

Copyright © 2014 Jiabao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The -dimensional folded hypercube is an important and attractive variant of the -dimensional hypercube , which is obtained from by adding an edge between any pair of vertices complementary edges. is superior to in many measurements, such as the diameter of which is , about a half of the diameter in terms of . The Kirchhoff index is the sum of resistance distances between all pairs of vertices in . In this paper, we established the relationships between the folded hypercubes networks and its three variant networks , , and on their Kirchhoff index, by deducing the characteristic polynomial of the Laplacian matrix in spectral graph theory. Moreover, the explicit formulae for the Kirchhoff indexes of , , , and were proposed, respectively.