Spectral arbitrariness for trees fails spectacularly

Fallat, Shaun M. (avtor), Hall, H. Tracy (avtor), Levene, Rupert H. (avtor), Meyer, Seth A. (avtor), Nasserasr, Shahla (avtor), Oblak, Polona (avtor), Šmigoc, Helena (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: spectrum, multiplicity lists, rooted trees, hedges, inverse eigenvalue problem for graphs
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FRI - Fakulteta za računalništvo in informatiko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2024
• Št. strani: Str. 161-210
• Številčenje: Vol. 169
• PID: 20.500.12556/RUL-160049
• UDK: 51
• ISSN pri članku: 0095-8956
• DOI: 10.1016/j.jctb.2024.06.007
• COBISS.SI-ID: 203133187
• Datum objave v RUL: 12.08.2024

Gradivo je del revije

• Naslov: Journal of combinatorial theory
• Skrajšan naslov: J. comb. theory, Ser. B
• Založnik: Elsevier
• ISSN: 0095-8956
• COBISS.SI-ID: 25721600

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: spekter, seznam večkratnosti, drevo s korenom, inverzni problem lastnih vrednosti za graf