The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter bounds the path cover number which is the minimum number of vertex-disjoint-induced paths that cover all the vertices of graph. In this paper, we investigate these two parameters and present an infinite number of graphs with the large difference between these two parameters and an infinite number of graphs with no difference between these parameters. Also, we prove a conjecture about the relationship between these parameters for some graphs.

中文翻译：

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关于某些图的零强迫数和路径覆盖数的关系

图的迫零数是迫零集的最小大小。此参数限制路径覆盖数，该数量是覆盖图的所有顶点的顶点不相交引起的路径的最小数量。在本文中，我们研究了这两个参数，并给出了无穷多个图，这两个参数之间的差异很大，以及无穷多个图，而这些参数之间没有差异。此外，对于某些图形，我们证明了这些参数之间的关系。