论文标题
最小零强迫集
Minimal Zero Forcing Sets
论文作者
论文摘要
在本文中，我们研究了最小（关于包容性）零强迫集。我们首先研究图何时可以在多项式或指数上具有许多不同的最小零强迫集。我们还研究了最小零强迫集的最大大小集合$ \ edline {\ pereratatorName {z}}}（g）$，并将其与零强迫number $ \ operatatorName {z}（g）$相关联。令人惊讶的是，我们表明，平等$ \叠加{\ operatorAtorName {z}}（g）= \ propatatorName {z}（g）$是通过删除通用顶点而不是通过添加通用顶点来保留的。我们还表征了$ \ overline {\ operatorName {z}}（g）$的极端值的图形，并探索$ \ overline {\ peripatorName {z}}}}（g）$和$ \ operatatorNAMe {z}}（z}（g）$之间的差距。
In this paper, we study minimal (with respect to inclusion) zero forcing sets. We first investigate when a graph can have polynomially or exponentially many distinct minimal zero forcing sets. We also study the maximum size of a minimal zero forcing set $\overline{\operatorname{Z}}(G)$, and relate it to the zero forcing number $\operatorname{Z}(G)$. Surprisingly, we show that the equality $\overline{\operatorname{Z}}(G)=\operatorname{Z}(G)$ is preserved by deleting a universal vertex, but not by adding a universal vertex. We also characterize graphs with extreme values of $\overline{\operatorname{Z}}(G)$ and explore the gap between $\overline{\operatorname{Z}}(G)$ and $\operatorname{Z}(G)$.
