路的Laplacian能控性的推广
Generalizing Laplacian Controllability of Paths
摘要：
众所周知，如果网络拓扑是路径或线，并且顶点或节点的状态根据共识策略演化，则网络是拉普拉斯可控的，其输入连接到其终端顶点。在这项工作中，一条路被认为是互联有限数量的两个顶点的反正则图，然后可能连接一个以上的顶点后的结果图。证明了路的单输入Laplacian能控性可以推广到任意正整数$k$，连接有限个$k$ -顶点反正则图的情形.给出了将这些反正则图连接起来的方法，以及选择连接单个输入的顶点使网络拉普拉斯可控的方法。
英文摘要：
It is well known that if a network topology is a path or line and the states of vertices or nodes evolve according to the consensus policy, then the network is Laplacian controllable by an input connected to its terminal vertex. In this work a path is regarded as the resulting graph after interconnecting a finite number of two-vertex antiregular graphs and then possibly connecting one more vertex. It is shown that the single-input Laplacian controllability of a path can be extended to the case of interconnecting a finite number of $k$-vertex antiregular graphs with or without one more vertex appended, for any positive integer $k$. The methods to interconnect these antiregular graphs and to select the vertex for connecting the single input that renders the network Laplacian controllable are presented as well.
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