A. Valyuzhenich

activity

20092021

most citedMinimum supports of eigenfunctions of Johnson graphs

2 citations · 4 across the 4 of their papers we have counts for

collaborators

9 papers

math.CO2021

Minimum supports of eigenfunctions of graphs: a survey

Ev Sotnikova, Alexandr Valyuzhenich

In this work we present a survey of results on the problem of finding the minimum cardinality of the support of eigenfunctions of graphs.

math.CO2020

Eigenfunctions and minimum 1-perfect bitrades in the Hamming graph

Alexandr Valyuzhenich

The Hamming graph $H (n, q)$ is the graph whose vertices are the words of length $n$ over the alphabet ${0, 1, \dots, q - 1}$ , where two vertices are adjacent if they differ in exactly…

math.CO2019★ 1 cited

Minimum supports of eigenfunctions with the second largest eigenvalue of the Star graph

Vladislav Kabanov, Elena V. Konstantinova, Leonid Shalaginov +1

The Star graph $S_{n}$ , $n \geq 3$ , is the Cayley graph on the symmetric group $S y m_{n}$ generated by the set of transpositions ${(12), (13), \dots, (1 n)}$ . In this work we study eigenfu…

math.CO2019

Equitable 2-partitions of the Hamming graphs with the second eigenvalue

Ivan Mogilnykh, Alexandr Valyuzhenich

The eigenvalues of the Hamming graph $H (n, q)$ are known to be $λ_{i} (n, q) = (q - 1) n - q i$ , $0 \leq i \leq n$ . The characterization of equitable 2-partitions of the Hamming graphs $H (n, q)$ …

math.DS2018

Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels

Sergey Agapov, Alexandr Valyuzhenich

In this paper the geodesic flow on a 2-torus in a non-zero magnetic field is considered. Suppose that this flow admits an additional first integral $F$ on $N + 2$ different energy le…

math.CO2018

$P I$ -eigenfunctions of the Star graphs

Sergey Goryainov, Vladislav Kabanov, Elena Konstantinova +2

We consider the symmetric group $Sym_{n}, n ⩾ 2$ , generated by the set $S$ of transpositions $(1 i), 2 ⩽ i ⩽ n$ , and the Cayley graph $S_n=Cay(\math…