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Theory of domination has been remained in the focus of many researchers because of its applications in a variety of fields such as linear algebra, optimization, social sciences, design of communication networks, and military surveillance. Many variants of domination models such as total domination, equitable domination, fractional domination, global domination are among mention a few. In this book, we have discussed chromatic transversal domination, total domination, total equitable domination. The concept of total equitable bondage number in graphs has been also introduced.