Spectra of the blow-up graphs
  Let $G$ be graph on $n$ vertices and $G^{(t)}$ its blow-up graph of order $t.$ In this paper, we determine all eigenvalues of the Laplacian and the signless Laplacian matrix of $G^{(t)}$ and its complement $\bar{G^{(t)}}.$ 
Carla Oliveira, Leonardo de Lima and Vladimir Nikiforov
math.SP