<![CDATA[ABSTARCT. Let be a subset of , with is a graph without isolated vertices. A subset of referred to double domination in if every vertex , such that every vertex in minimal adjacent with two element of . The minimum cardinality of domination set, total domination set, and double domination set in respectively is a is a domination number, total domination number, and double domination number denote respectively , , and . A double domination number in minimum is two and a double domination number in will not be more order () in , that . A domination number if add one vertex of domination in then the element of dimination number will not be more a double domination number in , that . In this final project examined the sum of bound of doubel domination number in Corona and product lexicographic of two graphs. The minimum cardinality of double domination in Corona is with is order in . Menwhile, the minimum cardinality of double domination in Product Lexicographic at most . ]]>
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