Maximal canonical graphs with seven nonzero eigenvalues

Abstract

In [3] and [4] A. Torgašev described all finite and infinite connected graphs having 3, 4 or 5 nonzero eigenvalues (not necessarily distinct). In the same papers he has given a general method how to describe all connected graphs with any fixed number of nonzero eigenvalues. In [2] M. Lepović applying his method described all finite connected graphs which have exactly 6 nonzero eigenvalues. We here describe all finite connected graphs with exactly 7 nonzero eigenvalues.