PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY

A maximal complete subgraph of G is a clique. The minimum (maximum) clique number ?=?(G) (?=?(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 ß_0=ß_0 (G). A graph G is well covered if i(G)=ß_0 (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 ?(G ¯ )=i(G).