Algebraic connectivity of layered path graphs under node deletion
Algebraic connectivity of layered path graphs under node deletion
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DOI：
10.1109/cdc51059.2022.9992940
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发表时间：
2022-04
期刊：
影响因子：
--
通讯作者：
Ryusei Yoshise;Kaoru Yamamoto
中科院分区：
文献类型：
--
作者：
Ryusei Yoshise;Kaoru Yamamoto
本文研究了层次结构图的节点删除与代数连通性之间的关系。为了刻画这种结构，引入了分层路径图及其(子)图锥的概念。这个问题是由一位领导者引导的移动机器人编队控制引起的。特别地，我们考虑了机器人可能离开网络导致节点和相关边被移除的场景。我们证明了上层至少有一个邻居的存在对于代数连通性不因节点删除而恶化是至关重要的。
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.