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In this paper we compute the \(P_3\)-forcing number of honeycomb network. A dynamic coloring of the vertices of a graph \(G\) starts with an initial subset \(S\) of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set \(S\) is called a forcing set of \(G\) if, by iteratively applying the forcing process, every vertex in G becomes colored. If the initial set \(S\) has the added property that it induces a subgraph of \(G\) whose components are all paths of length 3, then \(S\) is called a \(P_3\)-forcing set of \(G\). A Ps-forcing set of \(G\) of minimum cardinality is called the \(P_3\)-forcing number of G denoted by \(ZP_3(G)\).