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

Abstract

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.