The Zero Forcing Number of Quartic Circulant Graphs of Prime Order

Let \( G \) be a graph, the zero forcing number \( Z(G) \) is the minimum of \( |Z| \) over all zero forcing sets \( Z \subseteq V(G) \). In this paper, we are interested in studying the zero forcing number of quartic circulant graphs \( C_{p}\left(s,t\right) \), where \( p \) is an odd prime. Based on the fact that \( C_{p}\left(s,t\right) \cong C_{p}\left(1,q\right) \), we give the exact values of the zero forcing number of some specific quartic circulant graphs.