On Zero-Divisor Graph of the Ring $\frac{\mathbb{F}_p[u, v]}{\langle u^2,\, v^2, \, uv-vu\rangle}$

In this article, we study the zero-divisor graph of the commutative non-chain ring with identity $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p,$ where $u^2 = 0$, $v^2 = 0$, $uv = vu$, and $p$ is an odd prime. We determine several graph-theoretic properties of the associated zero-divisor graph $\Gamma(R)$, including clique number, chromatic number, vertex connectivity, edge connectivity, diameter, and girth. In addition, we compute certain topological indices of $\Gamma(R)$. Furthermore, we obtain the eigenvalues, energy, and spectral radius of the adjacency matrix, the Laplacian matrix and the Eccentricity matrix of $\Gamma(R)$.