Spectrum of a class of matrices and its applications
  In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix, distance (signless) Laplacian matrix, to obtain some known and new results. Moreover, we propose some problems for further research. 
Lihua You, Man Yang, JInxi Li, Liyong Ren
math.CO