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Spectral arbitrariness for trees fails spectacularly
ID
Fallat, Shaun M.
(
Author
),
ID
Hall, H. Tracy
(
Author
),
ID
Levene, Rupert H.
(
Author
),
ID
Meyer, Seth A.
(
Author
),
ID
Nasserasr, Shahla
(
Author
),
ID
Oblak, Polona
(
Author
),
ID
Šmigoc, Helena
(
Author
)
PDF - Presentation file. The content of the document unavailable until 30.09.2026.
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https://www.sciencedirect.com/science/article/pii/S0095895624000583?dg
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Abstract
Given a graph G, consider the family of real symmetric matrices with the property that the pattern of their nonzero off-diagonal entries corresponds to the edges of G. For the past 30 years a central problem has been to determine which spectra are realizable in this matrix class. Using combinatorial methods, we identify a family of graphs and multiplicity lists whose realizable spectra are highly restricted. In particular, we construct trees with multiplicity lists that require a unique spectrum, up to shifting and scaling. This represents the most extreme possible failure of spectral arbitrariness for a multiplicity list, and greatly extends all previously known instances of this phenomenon, in which only single linear constraints on the eigenvalues were observed.
Language:
English
Keywords:
spectrum
,
multiplicity lists
,
rooted trees
,
hedges
,
inverse eigenvalue problem for graphs
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FRI - Faculty of Computer and Information Science
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2024
Number of pages:
Str. 161-210
Numbering:
Vol. 169
PID:
20.500.12556/RUL-160049
UDC:
51
ISSN on article:
0095-8956
DOI:
10.1016/j.jctb.2024.06.007
COBISS.SI-ID:
203133187
Publication date in RUL:
12.08.2024
Views:
66
Downloads:
1
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Record is a part of a journal
Title:
Journal of combinatorial theory
Shortened title:
J. comb. theory, Ser. B
Publisher:
Elsevier
ISSN:
0095-8956
COBISS.SI-ID:
25721600
Licences
License:
CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:
http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:
The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Secondary language
Language:
Slovenian
Keywords:
spekter
,
seznam večkratnosti
,
drevo s korenom
,
inverzni problem lastnih vrednosti za graf
Projects
Funder:
Other - Other funder or multiple funders
Name:
Inverse eigenvalue problem for graphs
Funder:
Other - Other funder or multiple funders
Project number:
RGPIN–2019–03934
Name:
NSERC Discovery Grant
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0222
Name:
Algebra, teorija operatorjev in finančna matematika
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-3004
Name:
Hkratna podobnost matrik
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