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CONNECTED DOM-FORCING SETS IN GRAPHS
Keywords:
zero forcing number, connected zero forcing number, domination number, connected domination number, dom-forcing number, connected dom-forcing numberDOI:
https://doi.org/10.17654/0974165825046Abstract
In a graph $G$, a dominating set $D_f \subseteq V(G)$ is called a dom-forcing set if the sub-graph induced by $\left\langle D_f\right\rangle$ 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 $F_d(G)$. A connected dom-forcing set of a graph $G$, is a dom-forcing set of $G$ that induces a sub graph of $G$ which is connected. The connected dom-forcing number of $G$, $F_{c d}(G)$, is the minimum size of a connected dom-forcing set. This study delves into the concept of the connected dom-forcing number $F_{c d}(G)$, examining its properties and characteristics. Furthermore, it seeks to accurately determine $F_{c d}(G)$ for several well-known graphs and their graph products.
Received: July 2, 2025
Revised: September 1, 2025
Accepted: September 8, 2025
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