Normalized Laplacian spectrum of some subdivision-coronas of two regular graphs

Abstract

In this paper, we determine the full normalized Laplacian spectrum of the subdivision-vertex corona, subdivision-edge corona, subdivision-vertex neighbourhood corona and subdivision-edge neighbourhood corona of a connected regular graph with an arbitrary regular graph in terms of their normalized Laplacian eigenvalues. Moreover, applying these results, we find some non-regular normalized Laplacian cospectral graphs.

Keywords:

• Normalized Laplacian matrix
• subdivision-vertex corona
• subdivision-edge corona
• subdivision-vertex neighbourhood corona
• subdivision-edge neighbourhood corona

AMS Subject Classifications:

• 05C50
• 47A75

Acknowledgements

The authors are thankful to the referee and the editor for their valuable comments and suggestions which improved the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.