In this book, some notions are introduced about “Neutrosophic Duality”. Two chapters are devised as “Initial Notions”, and “Modified Notions”. New setting is introduced to study dual-dominating number and neutrosophic dual-dominating number arising from dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. Maximum number of dominated vertices, is a number which is representative based on those vertices. Maximum neutrosophic number of dominated vertices corresponded to dual-dominating set is called neutrosophic dual-dominating number. Forming sets from dominated vertices to figure out different types of number of vertices in the sets from dominated sets n in the terms of maximum number of vertices to get maximum number to assign to neutrosophic graphs is key type of approach to have these notions namely dual-dominating number and neutrosophic dual-dominating number arising from dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. Two numbers and one set are assigned to a neutrosophic graph, are obtained but now both settings lead to approach is on demand which is to compute and to find representatives of sets having largest number of dominated vertices from different types of sets in the terms of maximum number and maximum neutrosophic number forming it to get maximum number to assign to a neutrosophic graph.