The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph

In this paper we introduce a parameter Mm(G), defined as the maximum over the minimal multiplicities of eigenvalues among all symmetric matrices corresponding to a graph G. We develop basic properties of Mm(G) and compute it for several families of graphs.

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Bibliographic Details
Published in:Linear algebra and its applications 2017-01, Vol.512, p.48-70
Main Authors: Oblak, Polona, Šmigoc, Helena
Format: Article
Language:English
Subjects:
Eigenvalues
Graph
Graphs
Inverse problems
Linear algebra
Mathematical analysis
Matrix methods
Minimal rank
Multiplicity of an eigenvalue
Symmetric matrix
Symmetry
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Description
Summary:In this paper we introduce a parameter Mm(G), defined as the maximum over the minimal multiplicities of eigenvalues among all symmetric matrices corresponding to a graph G. We develop basic properties of Mm(G) and compute it for several families of graphs.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.09.014