Maximal Canonical Graphs with Seven Nonzero Eigenvalues

Mirjana Lazić

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.