-cospectrality and -energy in cographs. Issue 2 (1st February 2018) - Tura, Fernando
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.