Characterization of rings with genus two prime ideal sum graphs

Abstract

Let [Formula: see text] be a commutative ring with unity. The prime ideal sum graph of the ring [Formula: see text] is a simple undirected graph whose vertex set is the set of nonzero proper ideals of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is a prime ideal of [Formula: see text]. In this paper, we characterize all the finite non-local commutative rings whose prime ideal sum graph is of genus [Formula: see text].