Disconnected captive domination in graphs

In this paper, disconnected captive domination, a novel domination model in graphs is introduced. The proper subset of the vertices of a graph is a disconnected captive dominating set if it is a total dominating set each vertex in this set dominates at least one which doesn’t belong to the dominating set and , - is disconnected subgraph. The minimum cardinality over all disconnected captive dominating sets in is the disconnected captive domination number of denoted by ( ). Some bounds and properties of disconnected captive domination are studied with respect to order, size, minimum degree, and the maximum degree of a graph. The disconnected captive domination in complement graphs is discussed. Finally, the disconnected captive dominating set of paths and cycles are determined.