Dom-forcing sets in graphs

A dominating set $D_f\subseteq V(G)$ of vertices in a graph $G$ is called a \emph{dom-forcing set} if the sub-graph induced by $⟨D_f⟩$ must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing number of the graph $G$, denoted by $F_d(G)$. This article embarks on an exploration of the dom-forcing number of a graph $G$. Additionally, it delves into the precise determination of $F_d(G)$ for certain well-known graphs