Complete characterization of the spectrum of the co-maximal graph of Z_n

Characterize completely the spectrum of the co-maximal graph of the ring of integers modulo n, equivalently the generating graph of the cyclic group Z_n, including its adjacency and Laplacian spectra.

Background

The generating graph of Z_n is isomorphic to the co-maximal graph of the ring Z_n. Previous work had studied the adjacency and Laplacian spectra of this graph, but the paper states that a complete spectral characterization was not available. The paper therefore develops matrix decompositions and eigenvalue bounds, reducing much of the analysis to the square-free part of n, but does not resolve the full characterization problem.