Abstract
The distance Laplacian matrix of a connected graph G is defined to be where denotes the distance matrix of G and diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. Similarly, the distance signless Laplacian matrix of G is defined as In this paper, we present a large set of nonisomorphic graphs which are -cospectral. A simple construction of graphs which are nonisomorphic and |L|-cospectral, where |L| is the signless Laplacian matrix of G, is also presented. We finish this paper exhibiting nonisomorphic and -noncospectral graphs with same -energy.
Acknowledgements
The author wish to thank anonymous referees for their helpful comments and suggestions which improved the presentation of this article.
Notes
No potential conflict of interest was reported by the author.