A maximal complete subgraph of G is a clique. The minimum (maximum) clique number X=X(G) (ω = ω(G))is the order of a minimum (maximum) clique of G. A graph G is clique regular if every clique is of the same order. Two vertices are said to dominate each other if they are adjacent. A set S is a dominating set if every vertex in V- S is dominated by a vertex in S. Two vertices are independent if they are not adjacent. The independent domination number i = i(G) is the order of a minimum independent dominating set of G. The order of a maximum independent set is the independence number β0 = β0(G). A graph G is well covered if i(G) = β0(G). In this paper it is proved that a graph G is well covered if and only if G¯ is clique regular. We also show that X(G¯) = i(G).