Chain graphs are not spectrally determined

Two non isomorphic graphs G and H are said to be cospectral, if they share the same adjacency eigenvalues. In this paper, we use a recursive procedure for computing the characteristic polynomial of chain graphs in order to obtain infinitely many pairs of connected cospectral chain graphs. This result disproves a conjecture posed in [Czechoslovak Math. J. 70 (4) (2020), 1125-1138]. In addition we construct infinite families of bipartite graphs sharing the same spectrum.