In this paper, we study a dynamic coloring of the vertices of a graph G that 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 a zero forcing set of G if, by iteratively5 applying the forcing process, every vertex in G becomes colored. The zero forcing number of G is the minimum cardinality of a zero forcing set of G. In this paper, we prove that if \(G \ne K_4\) is a connected cubic graph, then the zero forcing number of G is bounded above by twice its domination number, where the domination number of G is the minimum cardinality of a set of vertices of G such that every vertex not in S is adjacent to some vertex in S.

在本文中，我们研究了图G的顶点的动态着色，该动态着色是从有色顶点的初始子集S开始，而所有其余顶点都是无色的。在每个离散的时间间隔，一个正好有一个未着色邻居的着色顶点将强制该未着色邻居着色。如果通过迭代应用强制过程，G中的每个顶点都变为彩色，则初始集合S为G的零强迫集合。的迫零数ģ是迫零组的最小基数ģ。在本文中，我们证明如果\（G \ ne K_4 \）是一个连通三次图，则零强迫数为ģ通过两次其控制数，其中的控制数上界ģ是一组顶点的最小基数ģ使得每个顶点不在小号相邻于一些顶点小号。