On the construction of cospectral graphs for the adjacency and the normalized Laplacian matrices

Abstract

In [A note about cospectral graphs for the adjacency and normalized Laplacian matrices. Linear Multilinear Algebra. 2010;58(3-4):387–390], Butler constructed a family of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. In this article, we extend this construction for generating larger classes of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. Also, we provide a couple of constructions of non-bipartite graphs, which are cospectral for the adjacency matrices but not necessarily for the normalized Laplacian matrices.

Keywords:

• Adjacency matrix
• normalized Laplacian matrix
• cospectral graphs

2010 AMS Subject Classification:

• 05C50

Acknowledgments

The authors would like to thank the handling editor and the anonymous reviewers for their careful reading of the manuscript. Their constructive criticism has greatly improved this manuscript. M. Rajesh Kannan would like to thank the Department of Science and Technology, India, for financial support through the projects MATRICS (MTR/2018/000986) and Early Career Research Award (ECR/2017/000643).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We would like to thank one of the reviewers for informing us about the updated version of Chung's book available at: http://www.math.ucsd.edu/∼fan/research/revised.html.

Additional information

Funding

M. Rajesh Kannan would like to thank the Science and Engineering Research Board (Department of Science and Technology, India), for financial support through the projects MATRICS (MTR/2018/000986) and Early Career Research Award (ECR/2017/000643).