Block Structure and Spectrum of Zero-Divisor Graphs of Lipschitz Quaternion Rings Modulo $n$

We study the adjacency spectra of zero-divisor graphs associated with Lipschitz quaternion rings modulo $n$. For an odd prime $p$, the identification $\mathbb{L}_p\cong M_2(\mathbb{F}_p)$ gives a kernel--image partition of the nonzero singular matrices and an explicit block representation of the adj