  In [Steve Butler. A note about cospectral graphs for the adjacency and
normalized Laplacian matrices. Linear Multilinear Algebra, 58(3-4):387-390,
2010.], Butler constructed a family of bipartite graphs, which are cospectral
for both the adjacency and the normalized Laplacian matrices. In this article,
we extend this construction for generating larger classes of bipartite graphs,
which are cospectral for both the adjacency and the normalized Laplacian
matrices. Also, we provide a couple of constructions of non-bipartite graphs,
which are cospectral for the adjacency matrices but not necessarily for the
normalized Laplacian matrices.
