Some results on resistance distances and resistance matrices

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.

Keywords:

• resistance distance
• Kirchhoff index
• Laplacian matrix
• generalized inverse

AMS Subject Classifications:

• 05C12
• 05C50
• 15A09

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.