On the Seidel spectrum of the total graphs of the rings of integers modulo <i>n</i>

In this paper, we study the Seidel spectrum of the total graph [Formula: see text] for various values of n. For [Formula: see text], with p prime, we give a complete spectral description and show that the spectrum is integral if and only if [Formula: see text]. When n is not a prime power, the zero-divisor set is no longer an ideal, requiring alternative methods, including explicit eigenvector construction. Using these techniques and computational verification, we determine the spectra for n of the forms [Formula: see text], [Formula: see text], and [Formula: see text] with distinct odd primes [Formula: see text]. Several illustrative examples are provided.