  In 2010, Butler introduced the unfolding operation on a bipartite graph to
produce two bipartite graphs, which are cospectral for the adjacency and the
normalized Laplacian matrices. In this article, we describe how the idea of
unfolding a bipartite graph with respect to another bipartite graph can be
extended to nonbipartite graphs. In particular, we describe how unfoldings
involving reflexive bipartite, semi-reflexive bipartite, and multipartite
graphs are used to obtain cospectral nonisomorphic graphs for the adjacency
matrix.
