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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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 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.
doi_str_mv 10.1016/j.laa.2016.09.014
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subjects Eigenvalues
Graph
Graphs
Inverse problems
Linear algebra
Mathematical analysis
Matrix methods
Minimal rank
Multiplicity of an eigenvalue
Symmetric matrix
Symmetry
title The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph
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