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For a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained: Theorem. If G does not have an induced subgraph isomorphic to K 1,3, then γ (G) = i (G).

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Cockayne, Dawes and Hedetneimi [6] obtained the following upper on the total domination number of a connected graph in terms of the order of the graph. Theorem (Cockayne, Dawes and Hedetneimi [6]) If G is a connected graph of order n ≥ 3, then γt (G) ≤ 2n 3. Brigham, Carrington, and Yitary [5] characterized the connected graphs of order at least 3 with total domination number exactly two-thirds their order.

For a survey on domination perfect graphs, we refer the reader to. Well-covered graphs. A graph is well-covered if the independent domination number is equal to the independence number.

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