Digraphs with real and gaussian spectra

The conventional binary operations of cartesian product, conjunction, and composition of two digraphs D, and D2 are observed to give the sum, the product, md a more complicated combination of the spectra of D1 and Dz as the resulting spectrum. These formulas for analyzing the spectrum of a digraph are utilized to construct for any positive integer PI, a collection of n nonisomorphic strung reguhw nonsymmetric digraphs with real sptxtra. Fu,rther, an infinite collection of strong nonsymmetric digraphs with nonzero gaussian integer value3 is found. Finally, for any n, it is shown that there are n cospectral strong nonsymmetric digraphs with integral spectra.