Return to search

Nodal Domain Theorems and Bipartite Subgraphs

The Discrete Nodal Domain Theorem states that an eigenfunction of the k-th largest eigenvalue of a generalized graph Laplacian has at most k (weak) nodal domains. We show that the number of strong nodal domains cannot exceed the size of a maximal induced bipartite subgraph and that this bound is sharp for generalized graph Laplacians. Similarly, the number of weak nodal domains is bounded by the size of a maximal bipartite minor.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:32149
Date09 November 2018
CreatorsBiyikoglu, Türker, Leydold, Josef, Stadler, Peter F.
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess
Relation1081-3810, 21

Page generated in 0.002 seconds