Let R be a commutative ring with identity. The comaximal graph of R, denoted by \(\Gamma (R)\) , is the simple graph whose vertex set is R and in which two distinct vertices x and y are adjacent if and only if \(xR+yR=R\) . In this paper, we study the comaximal graph associated with the residue class ring \(\mathbb {Z}_{n}\) . We determine the eigenvalues and eigenvectors of \(\Gamma (\mathbb {Z}_{n})\) , and investigate its spectral structure in detail. In particular, we characterize those comaximal graphs \(\Gamma (\mathbb {Z}_{n})\) whose spectrum has no repeated eigenvalues. Moreover, using an equitable partition, we compute the determinant and the trace of the square of the corresponding quotient matrix. As an application of these computations, we derive explicit and sharp bounds for the energy of \(\Gamma (\mathbb {Z}_{n})\) . We conclude with remarks and directions for further research.
