Comaximal graph of commutative rings

Let R be a commutative ring with identity. Let F(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 Gamma(2)(R) of Gamma(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 Gamma(2)(R)\J(R). In addition, it is shown that for two finite semi-local rings R and S, if R is reduced, then Gamma(R) congruent to Gamma(S) if and only if R congruent to S. (C) 2007 Published by Elsevier Inc.