论文标题
零强迫具有功率法律分配的图形数
Zero forcing number of graphs with a power law degree distribution
论文作者
论文摘要
零强制数是遵循单个邻居颜色强迫规则的最小黑色顶点的最小数量，可以将白色图形为黑色。零强制数提供了有关图形上线性代数的拓扑信息，并应用了线性动力学系统的可控性和图形上的量子步行以及其他问题。在这里，我研究了具有功率法律分布的无向简单图的零强制数$ p_k \ sim k^{ - γ} $。对于优先附件模型生成的图形，并具有图形大小的直径比对数，当$γ\ rightarrow2 $时，零强迫号接近图形大小。相反，对于由停用模型生成的图，其直径与图形大小线性缩放，零强制数小于图形大小，独立于$γ$。因此，图形大小的图表的缩放是决定动态系统可控性的另一个因素。
The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbour colour forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of linear dynamical systems and quantum walks on graphs among other problems. Here, I investigate the zero forcing number of undirected simple graphs with a power law degree distribution $p_k\sim k^{-γ}$. For graphs generated by the preferential attachment model, with a diameter scaling logarithmically with the graph size, the zero forcing number approaches the graph size when $γ\rightarrow2$. In contrast, for graphs generated by the deactivation model, with a diameter scaling linearly with the graph size, the zero forcing number is smaller than the graph size independently of $γ$. Therefore the scaling of the graph diameter with the graph size is another factor determining the controllability of dynamical systems.
