On a New Extension of the Zero-Divisor Graph

Abstract

In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R, and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R, x and y are adjacent if and only if xy = 0 or x + y ∈ Z(R). We present some properties and examples of this graph, and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.