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 $\langle D_{ f} \rangle$ 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
Categories: math.CO