Entries of the group inverse of the Laplacian matrix for generalized Johnson graphs

Abstract

In this paper, we use graph theoretic properties of generalized Johnson graphs to compute the entries of the group inverse of Laplacian matrices for generalized Johnson graphs. We then use these entries to compute the Zenger function for the group inverse of Laplacian matrices of generalized Johnson graphs.

Keywords:

• Johnson graph
• Laplacian matrix
• group inverse
• Zenger function

AMS Subject Classification:

• 05C50

Acknowledgements

The author would like to thank the anonymous referee for his or her many valuable suggestions which improved the quality of this paper.

Notes

No potential conflict of interest was reported by the author.

1 For more background material on nonnegative matrices and M-matrices see Berman and Plemmons [10].