Zobrazeno 1 - 10
of 2 133
pro vyhledávání: '"Vorob’ev, P."'
Autor:
Vorob'ev, Konstantin
We consider extended $1$-perfect codes in Hamming graphs $H(n,q)$. Such nontrivial codes are known only when $n=2^k$, $k\geq 1$, $q=2$, or $n=q+2$, $q=2^m$, $m\geq 1$. Recently, Bespalov proved nonexistence of extended $1$-perfect codes for $q=3$, $4
Externí odkaz:
http://arxiv.org/abs/2403.10992
We obtain a classification of the completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs H(3,q) up to q and intersection array. Due to works of Meyerowitz, Mogilnykh and Valyuzenich, our result completes the c
Externí odkaz:
http://arxiv.org/abs/2403.02702
Autor:
Landjev, Ivan, Vorob'ev, Konstantin
We consider the problem of finding $A_2(n,\{d_1,d_2\})$ defined as the maximal size of a binary (non-linear) code of length $n$ with two distances $d_1$ and $d_2$. Binary codes with distances $d$ and $d+2$ of size $\sim\frac{n^2}{\frac{d}{2}(\frac{d}
Externí odkaz:
http://arxiv.org/abs/2402.13420
We study nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and the Johnson graphs. For the first eigenvalue we obtain the minimums of $L_{\infty}$-norm for several infinite series of Johnson graphs, including J(n,3) as w
Externí odkaz:
http://arxiv.org/abs/2304.00922
Autor:
Mogilnykh, I. Yu., Vorob'ev, K. V.
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 interrelation of these codes, a complete characterization of the completely reg
Externí odkaz:
http://arxiv.org/abs/2210.11184
We finish the classification of equitable 2-partitions of the Johnson graphs of diameter 3, $J(n,3)$, for $n>10$.
Externí odkaz:
http://arxiv.org/abs/2206.15341
A graph $G$ on $n$ vertices of diameter $D$ is called $H$-palindromic if $\alpha(G,k) = \alpha(G,D-k)$ for all $k=0, 1, \dots, \left \lfloor{\frac{D}{2}}\right \rfloor$, where $\alpha(G,k)$ is the number of unordered pairs of vertices at distance $k$
Externí odkaz:
http://arxiv.org/abs/2112.11164
Autor:
L.V. Rozhkova, V.P. Vorob'ev
Publikováno v:
Известия высших учебных заведений. Поволжский регион: Общественные науки, Iss 4 (2024)
Background. 2022 – the beginning of Russia’s special military operation in Ukraine, when there were dramatic shifts in political, socio-economic and socio-cultural spheres that affected the entire Russian society and showed significant “margin
Externí odkaz:
https://doaj.org/article/a15abb6910f04c6cba4d0fa8999a0cd1
Autor:
Akhmejanova, Margarita, Olmezov, Konstantin, Volostnov, Aleksei, Vorobyev, Ilya, Vorob'ev, Konstantin, Yarovikov, Yury
The Wiener index $W(G)$ of a connected graph $G$ is a sum of distances between all pairs of vertices of $G$. In 1991, \v{S}olt\'{e}s formulated the problem of finding all graphs $G$ such that for every vertex $v$ the equation $W(G)=W(G-v)$ holds. The
Externí odkaz:
http://arxiv.org/abs/2012.08786
Autor:
Vorob'ev, Konstantin
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, we find all admissible quotient matrices of such partitions, and cha
Externí odkaz:
http://arxiv.org/abs/2003.10956