Distinct eigenvalues of the Transposition graph

2023/06/02 by Elena V. Konstantinova, Konstantinova, Elena V., Artem Kravchuk +1 · 2 citations
Engineering · Mathematics · #05C25 #05E10 #05E15 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Representation Theory (math.RT) #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2306.01627

openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Transposition graph T_n is defined as a Cayley graph over the symmetric group generated by all transpositions. It is known that all eigenvalues of T_n are integers. Moreover, zero is its eigenvalue for any n\geqslant 4. But the exact distribution of the spectrum of the graph T_n is unknown. In this paper we prove that integers from the interval [-(n-4)/(2), (n-4)/(2)] lie in the spectrum of T_n if n \geqslant 19.

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• Graphical Designs find Combinatorial Structures
• Proof of a conjecture on eigenvalues of transposition graph

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