In this paper, a disconnected domination model in graph theory, known as doubly disconnected domination, is introduced. Suppose that be a simple, undirected, finite and nontrivial graph. A subset is called doubly disconnected dominating set in if is dominating set and both the induced subgraphs and are disconnected subgraphs. The least cardinality among all doubly disconnected dominating sets of is the doubly disconnected domination number . This study investigates various bounds and properties of this domination parameter to give the relations between and the maximum degree in , minimum degree, the size and the order of the graph. Some results are given in this paper to explain and prove the doubly disconnected domination number for any graph constructed by corona or join operations. Furthermore, is discussed and evaluated for some well-known graphs, while other graphs are proved to be hasn't this type of domination.
Dahham et al. (2025) studied this question.