论文标题
节点删除下分层路径图的代数连接性
Algebraic connectivity of layered path graphs under node deletion
论文作者
论文摘要
本文研究了由层代表的层次结构的图表的节点缺失与代数连接性之间的关系。为了捕获这种结构，引入了分层路径图及其（子）图锥的概念。该问题是由由领导者指导的移动机器人形成控制的动机。特别是，我们考虑了一种场景，在这种情况下，机器人可能会离开网络，从而导致删除节点和相关的边缘。我们表明，上层中至少一个邻居的存在对于不通过节点删除而恶化的代数连接至关重要。
This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are introduced. The problem is motivated by a mobile robot formation control guided by a leader. In particular, we consider a scenario in which robots may leave the network resulting in the removal of the nodes and the associated edges. We show that the existence of at least one neighbor in the upper layer is crucial for the algebraic connectivity not to deteriorate by node deletion.
