Zobrazeno 1 - 10
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pro vyhledávání: '"Vorob'ëv AS"'
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
Publikováno v:
In Discrete Mathematics February 2025 348(2)
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:
Vinogradova, Katerina A., Berezin, Aleksey S., Taigina, Marina D., Sannikova, Victoriya A., Filippov, Igor R., Pervukhina, Natalia V., Yu. Naumov, Dmitrii, Kolybalov, Dmitry S., Vorob'ev, Aleksey Yu.
Publikováno v:
In Inorganica Chimica Acta 1 September 2024 569
Publikováno v:
In Discrete Applied Mathematics 15 February 2024 344:154-160