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Linear and Multilinear Algebra Volume 63, 2015 - Issue 3
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Articles

Some results on resistance distances and resistance matrices

Lizhu SunSchool of Science, Harbin Institute of Technology, Harbin, P.R. China.
,
Wenzhe WangCollege of Science, Harbin Engineering University, Harbin, P.R. China.
,
Jiang ZhouCollege of Science, Harbin Engineering University, Harbin, P.R. China.;College of Computer Science and Technology, Harbin Engineering University, Harbin, P.R. China.Correspondence[email protected]
&
Changjiang BuCollege of Science, Harbin Engineering University, Harbin, P.R. China.Correspondence[email protected]
Pages 523-533 | Received 23 Sep 2013, Accepted 11 Dec 2013, Published online: 11 Jun 2014
 
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Abstract

In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix.

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Acknowledgements

The authors would like to thank the referee for giving helpful suggestions.

Notes

1 This work is supported by the National Natural Science Foundation of China under [grant number 11371109], and the Fundamental Research Funds for the Central Universities.

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