TY - JOUR

T1 - Distinct eigenvalues of the Transposition graph

AU - Konstantinova, Elena V.

AU - Kravchuk, Artem

N1 - The study by Elena V. Konstantinova was performed according to the Government research assignment for IM, SB RAS, project FWNF-2022-0017. The work of Artem Kravchuk was supported by the Mathematical Center in Akademgorodok, under agreement No. 075-15-2022-281 with the Ministry of Science and High Education of the Russian Federation.

PY - 2024/6/1

Y1 - 2024/6/1

N2 - Transposition graph Tn is defined as a Cayley graph over the symmetric group generated by all transpositions. It is known that all eigenvalues of Tn are integers. Moreover, zero is its eigenvalue for any n⩾4. But the exact distribution of the spectrum of the graph Tn is unknown. In this paper we prove that integers from the interval [Formula presented] lie in the spectrum of Tn for any n⩾19.

AB - Transposition graph Tn is defined as a Cayley graph over the symmetric group generated by all transpositions. It is known that all eigenvalues of Tn are integers. Moreover, zero is its eigenvalue for any n⩾4. But the exact distribution of the spectrum of the graph Tn is unknown. In this paper we prove that integers from the interval [Formula presented] lie in the spectrum of Tn for any n⩾19.

KW - Integral graph

KW - Spectrum

KW - Transposition graph

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85188832201&origin=inward&txGid=4a913af74e77b3a219d36f4194977735

UR - https://www.elibrary.ru/item.asp?id=67166592

UR - https://www.mendeley.com/catalogue/1a44390d-c0bc-3857-9940-c75017d050bc/

U2 - 10.1016/j.laa.2024.03.011

DO - 10.1016/j.laa.2024.03.011

M3 - Article

VL - 690

SP - 132

EP - 141

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -