Comaximal graph of commutative rings

Abstract Let R be a commutative ring with identity. Let Γ ( R ) be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if R a + R b = R . In this paper we consider a subgraph Γ 2 ( R ) of Γ ( R ) which consists of non-unit elements. We look at the connectedness and the diameter of this graph. We completely characterize the diameter of the graph Γ 2 ( R ) ∖ J ( R ) . In addition, it is shown that for two finite semi-local rings R and S, if R is reduced, then Γ ( R ) ≅ Γ ( S ) if and only if R ≅ S .