K. Vorob'ev

activity

20172022

most citedMinimum supports of functions on the Hamming graphs with spectral constraints

14 citations · 39 across the 10 of their papers we have counts for

collaborators

10 papers

math.CO2022

On completely regular codes with minimum eigenvalue in geometric graphs

I. Yu. Mogilnykh, K. V. Vorob'ev

We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrela…

math.CO2022★ 2 cited

Equitable 2-partitions of the Johnson graphs $J (n, 3)$

Rhys J. Evans, Alexander L. Gavrilyuk, Sergey Goryainov +1

We finish the classification of equitable 2-partitions of the Johnson graphs of diameter 3, $J (n, 3)$ , for $n > 10$ .

math.CO2021

On the palindromic Hosoya polynomial of trees

Dmitry Badulin, Alexandr Grebennikov, Konstantin Vorob'ev

A graph $G$ on $n$ vertices of diameter $D$ is called $H$ -palindromic if $α (G, k) = α (G, D - k)$ for all $k = 0, 1, \dots, ⌊ \frac{D}{2} ⌋$ , where $α (G, k)$ is th…

math.CO2020★ 1 cited

Wiener index and graphs, almost half of whose vertices satisfy Šoltés property

Margarita Akhmejanova, Konstantin Olmezov, Aleksei Volostnov +3

The Wiener index $W (G)$ of a connected graph $G$ is a sum of distances between all pairs of vertices of $G$ . In 1991, Šoltés formulated the problem of finding all graphs $G$ such t…

math.CO2020★ 4 cited

Equitable 2-partitions of Johnson graphs with the second eigenvalue

Konstantin Vorob'ev

We study equitable 2-partitions of the Johnson graphs J(n,w) with a quotient matrix containing the eigenvalue lambda_2(w,n) = (w-2)(n-w-2)-2 in its spectrum. For any w>=4 and n>=2w…

math.CO2019★ 13 cited

Perfect 2-colorings of Hamming graphs

Evgeny A. Bespalov, Denis S. Krotov, Aleksandr A. Matiushev +2

We consider the problem of existence of perfect $2$ -colorings (equitable $2$ -partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs a…

math.CO2018

On reconstruction of eigenfunctions of Johnson graphs

Konstantin Vorob'ev

In the present work we consider the problem of a reconstruction of eigenfunctions of the Johnson graph $J (n, w)$ . We give necessary and sufficient numerical conditions for a unique…

math.CO2018★ 3 cited

On unbalanced Boolean functions with best correlation immunity

Denis S. Krotov, Konstantin V. Vorob'ev

It is known that the order of correlation immunity of a nonconstant unbalanced Boolean function in $n$ variables cannot exceed $2 n /3 - 1$ ; moreover, it is $2 n /3 - 1$ if and only if the…

math.CO2018★ 14 cited

Minimum supports of functions on the Hamming graphs with spectral constraints

Alexandr Valyuzhenich, Konstantin Vorob'ev

We study functions defined on the vertices of the Hamming graphs $H (n, q)$ . The adjacency matrix of $H (n, q)$ has $n + 1$ distinct eigenvalues $n (q - 1) - q \cdot i$ with corresponding eige…

math.CO2017★ 2 cited

Minimum supports of eigenfunctions of Johnson graphs

Konstantin Vorob'ev, Ivan Mogilnykh, Alexandr Valyuzhenich

We study the weights of eigenvectors of the Johnson graphs $J (n, w)$ . For any $i \in {1, \dots, w}$ and sufficiently large $n, n \geq n (i, w)$ we show that an eigenvector of $J (n, w)$ …