Geodesic
Constructing segments of quadratic length in $Spec(T_n)$ through segments of linear length
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 927-939 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Transposition graph $T_n$ is defined as a Cayley graph over the symmetric group $Sym_n$ generated by all transpositions. It is known that the spectrum of $T_n$ consists of integers, but it is not known exactly how these numbers are distributed. In this paper we prove that integers from the segment $[-n, n]$ lie in the spectrum of $T_n$ for any $n\geqslant 31$. Using this fact we also prove the main result of this paper that a segment of quadratic length with respect to $n$ lies in the spectrum of $T_n$.
Keywords: integral graph, spectrum.
Mots-clés : Transposition graph 
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A. V. Kravchuk. Constructing segments of quadratic length in $Spec(T_n)$ through segments of linear length. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 927-939. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a8/

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