Connected Dom-Forcing Sets in Graphs

In a graph , a dominating set is called a dom-forcing set if the sub-graph induced by must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing number of the graph , denoted by . A connected dom-forcing set of a graph , is a dom-forcing set of that induces a sub graph of which is connected. The connected dom-forcing number of , , is the minimum size of a connected dom-forcing set. This study delves into the concept of the connected dom-forcing number , examining its properties and characteristics. Furthermore, it seeks to accurately determine for several well-known graphs and their graph products.