TOPOLOGICAL INDICES, SPECTRA AND ENERGIES OF PRIME IDEAL SUM GRAPHS OF COMMUTATIVE RINGS

Abstract

Let R be a commutative ring with 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 f ind out the topological indices, spectra and energies of the prime ideal sum graphs of Zn, where n = pα, pq, p2q, p2q2, pqr, p3q, pqrs; p, q, r, s being distinct prime integers, α ∈ Z+ and Zn is the ring of integers modulo n.