The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Charles R. Johnson; Carlos Manuel Saiago

doi:10.1016/j.disc.2005.04.026

The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Charles R. Johnson, Carlos Manuel Saiago

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Abstract

Among those real symmetric matrices whose graph is a given tree $T$, the maximum multiplicity is known to be the path cover number of $T$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are $1$.

Original language	English
Pages (from-to)	3130-3135
Number of pages	6
Journal	Discrete Mathematics
Volume	306
Issue number	23(SI)
DOIs	https://doi.org/10.1016/j.disc.2005.04.026
Publication status	Published - 6 Dec 2006

Keywords

Real symmetric matrices
Eigenvalues
Multiplicities
Maximum multiplicity
Trees
NIM trees
Vertex degrees

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title = "The trees for which maximum multiplicity implies the simplicity of other eigenvalues",

abstract = "Among those real symmetric matrices whose graph is a given tree \$T\$, the maximum multiplicity is known to be the path cover number of \$T\$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are \$1\$.",

keywords = "Real symmetric matrices, Eigenvalues, Multiplicities, Maximum multiplicity, Trees, NIM trees, Vertex degrees",

author = "Johnson, \{Charles R.\} and Saiago, \{Carlos Manuel\}",

year = "2006",

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T1 - The trees for which maximum multiplicity implies the simplicity of other eigenvalues

AU - Johnson, Charles R.

AU - Saiago, Carlos Manuel

PY - 2006/12/6

Y1 - 2006/12/6

N2 - Among those real symmetric matrices whose graph is a given tree $T$, the maximum multiplicity is known to be the path cover number of $T$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are $1$.

AB - Among those real symmetric matrices whose graph is a given tree $T$, the maximum multiplicity is known to be the path cover number of $T$. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are $1$.

KW - Real symmetric matrices

KW - Eigenvalues

KW - Multiplicities

KW - Maximum multiplicity

KW - Trees

KW - NIM trees

KW - Vertex degrees

U2 - 10.1016/j.disc.2005.04.026

DO - 10.1016/j.disc.2005.04.026

M3 - Article

SN - 0012-365X

VL - 306

SP - 3130

EP - 3135

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 23(SI)

ER -

The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Abstract

Keywords

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