A super-Cayley graph's spectrum is a super-Fourier transform of its connection set; for Frobenius rings this yields explicit spectral formulas and rationality criteria.
Carlitz, A theorem on permutations in a finite field, Proceedings of the American Mathematical Society 11 (1960), no
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Supercharacters of finite abelian groups and applications to spectra of $U$-unitary Cayley graphs
A super-Cayley graph's spectrum is a super-Fourier transform of its connection set; for Frobenius rings this yields explicit spectral formulas and rationality criteria.