Topological indices, spectra and energies of prime ideal sum graphs of commutative rings

Abstract

Let R be a commutative ring with the nonzero identity. The prime ideal sum graph of R, denoted by PIS(R), is a graph whose vertex-set is the set of all nonzero proper ideals of R, and two distinct vertices I and J are adjacent if and only if I + J is a prime ideal of R. In this study, our aim is to find out the topological indices, spectra and energies of the prime ideal sum graphs of \mathbb{Z}_n , where n = p^{α}, pq, p^{2}q, p^{2}q^{2}, pqr, p^{3}q, p^{2}qr, pqrs ; p, q, r, s being distinct prime integers, α ∈ \mathbb{Z}^{+} and \mathbb{Z}_{n} is the ring of integers modulo n.