5 citations · 8 across the 9 of their papers we have counts for
10 papers
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.
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_…
On Jacobian group of the -graph
Alexander Mednykh, Ilya Mednykh, Ivan Yudin
In the present paper we compute the Jacobian group of -graph The notion of -graph continues the list of families of -, - and -graphs well-known in t…
On Jacobian group and complexity of the Y-graph
Y. S. Kwon, A. D. Mednykh, I. A. Mednykh
In the present paper we suggest a simple approach for counting Jacobian group of the -graph In the case the structure of the Jacobian group will…
The number of rooted forests in circulant graphs
L. A. Grunwald, I. A. Mednykh
In this paper, we develop a new method to produce explicit formulas for the number of rooted spanning forests in the circulant graphs and…
Complexity of the circulant foliation over a graph
Young Soo Kwon, Alexander Mednykh, Ilya Mednykh
In the present paper, we investigate the complexity of infinite family of graphs obtained as a circulant foliation over a graph on vertices…
Complexity of circulant graphs with non-fixed jumps, its arithmetic properties and asymptotics
Alexander Mednykh, Ilya Mednykh
In the present paper, we investigate a family of circulant graphs with non-fixed jumps $$G_n=C_{βn}(s_1, \ldots,s_k,α_1n,\ldots,α_\ell n),\, 1\le s_1<\ldots<s_k\le[\frac{βn}{2}],\,…
On rationality of generating function for the number of spanning trees in circulant graphs
A. D. Mednykh, I. A. Mednykh
Let be the generating function for the number of spanning trees in the circulant graphs We show that $F(x…
On complexity of cyclic coverings of graphs
Y. S. Kwon, A. D. Mednykh, I. A. Mednykh
By complexity of a finite graph we mean the number of spanning trees in the graph. The aim of the present paper is to give a new approach for counting complexity of cyclic $…
The number of spanning trees in circulant graphs, its arithmetic properties and asymptotic
Alexander Mednykh, Ilya Mednykh
In this paper, we develop a new method to produce explicit formulas for the number of spanning trees in the undirected circulant graphs and $C_{2…