Bipartite graphs with all but two eigenvalues equal to 0 and 1

In this paper we study the class G of all connected bipartite graphs whose adjacency spectrum, apart from the maximum and the minimum eigenvalue, just contains 0 and +/- 1. It turns out that G consists of five infinite families, each of them containing an infinite subfamily of integral graphs, and seven sporadic graphs. Moreover, we find all graphs in G determined by their spectrum and identify the cospectral mates of the remaining ones.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).