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.

引用

页码：803 / 819

页数：16

共 50 条

[41] A new lower bound on the independence number of graphs
Angel, Eric
Campigotto, Romain
Laforest, Christian
[J]. DISCRETE APPLIED MATHEMATICS, 2013, 161 (06) : 847 - 852
[42] LOWER BOUND NUMBER OF IRREDUCIBLE GRAPHS ON SURMCES
刘莹
刘彦佩
[J]. Acta Mathematica Scientia, 1998, (03) : 333 - 339
[43] A lower bound for the convexity number of some graphs
Kim B.K.
[J]. Journal of Applied Mathematics and Computing, 2004, 14 (1-2) : 185 - 191
[44] A lower bound on the multichromatic number of Kneser graphs
Osztenyi, Jozsef
[J]. ACTA SCIENTIARUM MATHEMATICARUM, 2008, 74 (1-2): : 289 - 296
[45] Sharp lower bounds on the metric dimension of circulant graphs
Knor, Martin
Skrekovski, Riste
Vetrik, Tomas
[J]. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2023,
[46] A lower bound for metric 1-median selection
Chang, Ching-Lueh
[J]. JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2017, 84 : 44 - 51
[47] Bound states of the NLS equation on metric graphs with localized nonlinearities
Serra, Enrico
Tentarelli, Lorenzo
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (07) : 5627 - 5644
[48] On the lack of bound states for certain NLS equations on metric graphs
Serra, Enrico
Tentarelli, Lorenzo
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 145 : 68 - 82
[49] Lower bound for the discrete norm of a polynomial on the circle
Dubinin, V. N.
[J]. MATHEMATICAL NOTES, 2011, 90 (1-2) : 284 - 287
[50] Lower bound for the discrete norm of a polynomial on the circle
V. N. Dubinin
[J]. Mathematical Notes, 2011, 90

← 1 2 3 4 5 →