on zero-divisor graph of the ring fp + ufp + u²fp

In this article, we discussed the zero-divisor graph of a commutative ring with identity fp + ufp + u²fp where u³ = 0 and p is an odd prime. we find the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth of a zero-divisor graph associated with the ring. we find some of topological indices and the main parameters of the code derived from the incidence matrix of the zero divisor graph γ(r). also, we find the eigenvalues, energy and spectral radius of both adjacency and laplacian matrices of γ(r).