Comaximal graph of commutative rings

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 Ra+Rb=R. In this paper we consider a subgraph Γ2(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 Γ2(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.