Abstract. Let R be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph Ω(R) whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if the product of the co-ideals generated by x and y is R. Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph Γ(R) and Ω(R).
