cospectrality and -energy in cographs

• Published in: Linear & multilinear algebra Vol. 66; no. 2; pp. 398 - 409
• Main Author: Tura, Fernando
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-02-2018; Taylor & Francis Ltd
• Subjects: 15A18; cographs; distance Laplacian matrix; distance signless Laplacian matrix; Eigenvalue; Graphs
• ISSN: 0308-1087; 1563-5139
• DOI: 10.1080/03081087.2017.1300230

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.