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Italian Domination in Complementary Prisms
Let be any graph and let be its complement. The complementary prism of is formed from the disjoint union of a graph and its complement by adding the edges of a perfect matching between the corresponding vertices of and . An Italian dominating function on a graph is a function such that and for each vertex for which , it holds that . The weight of an Italian dominating function is the value . The minimum weight of all such functions on is called the Italian domination number. In this thesis we will study Italian domination in complementary prisms. First we will present an error found in one of the references. Then we will define the small values of the Italian domination in complementary prisms, find the value of the Italian domination number in specific families of graphs complementary prisms, and conclude with future problems
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