Distinct eigenvalues of the Transposition graph

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 pro...

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Bibliographic Details
Published in:Linear algebra and its applications 2024-06, Vol.690, p.132-141
Main Authors: Konstantinova, Elena V., Kravchuk, Artem
Format: Article
Language:English
Subjects:
Integral graph
Spectrum
Transposition graph
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Summary: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 [−n−42,n−42] lie in the spectrum of Tn for any n⩾19.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2024.03.011