A Lower Bound for Nodal Count on Discrete and Metric Graphs

被引：0
|
作者：
Gregory Berkolaiko
机构：
[1] Texas A&M University,Department of Mathematics
来源：
Communications in Mathematical Physics | 2008年 / 278卷
关键词：
Directed Edge; Outgoing Edge; Nodal Count; Boundary Vertex; Quantum Graph;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the number of nodal domains (maximal connected regions on which a function has constant sign) of the eigenfunctions of Schrödinger operators on graphs. Under a certain genericity condition, we show that the number of nodal domains of the nth eigenfunction is bounded below by n  −  ℓ, where ℓ is the number of links that distinguish the graph from a tree.
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页码：803 / 819
页数：16
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