The Kirchhoff Index of Hypercubes and Related Complex Networks

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 formul...

Full description

Saved in:
Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2013-01, Vol.2013 (2013), p.235-241-127
Main Authors: Liu, Jia-Bao, Cao, Jinde, Pan, Xiang-Feng, Elaiw, A. M.
Format: Article
Language:English
Subjects:
Dynamics
Electric resistance
Graph theory
Mathematical research
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2013/543189