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math.CO2024
One can hear a discrete rectangular torus
A. D. Mednykh, I. A. Mednykh, G. K. Sokolova
In the present paper, we prove that two discrete rectangular tori are isospectral if and only if they are isomorphic.
math.CO2023
On the complexity of Cayley graphs on a dihedral group
Bobo Hua, Alexander Mednykh, Ilya Mednykh +1
In this paper, we investigate the complexity of an infinite family of Cayley graphs $\mathcal{D}_{n}=Cay(\mathbb{D}_{n}, b^{\pmβ_1},b^{\pmβ_2},\ldots,b^{\pmβ_s}, a b^{γ_1}, a b^{γ_…
math.CO2021
On the structure of Laplace characteristic polynomial for circulant foliation
Young Soo Kwon, Alexander Mednykh, Ilya Mednykh
In this paper, we describe the structure of the Laplace characteristic polynomial for the infinite family of graphs obtained as a circulant…