13 citations · 18 across the 7 of their papers we have counts for
7 papers
norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
E. A. Bespalov, I. Yu. Mogilnykh, K. V. Vorob'ev
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 -nor…
On extended 1-perfect bitrades
Evgeny A. Bespalov, Denis S. Krotov
Extended -perfect codes in the Hamming scheme can be equivalently defined as codes that turn to -perfect codes after puncturing in any coordinate, as completely regu…
On the non-existence of extended perfect codes and some perfect colorings
Evgeny Bespalov
In this paper we obtain the necessary condition for the existence of perfect -colorings (equitable -partitions) in Hamming graphs , where and Doob graphs $D…
Perfect 2-colorings of Hamming graphs
Evgeny A. Bespalov, Denis S. Krotov, Aleksandr A. Matiushev +2
We consider the problem of existence of perfect -colorings (equitable -partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs a…
MDS codes in the Doob graphs
Evgeny Bespalov, Denis Krotov
The Doob graph , where , is the direct product of copies of The Shrikhande graph and copies of the complete graph on vertices. The Doob graph $D(m,n)…
Distance-2 MDS codes and latin colorings in the Doob graphs
Denis Krotov, Evgeny Bespalov
The maximum independent sets in the Doob graphs D(m,n) are analogs of the distance-2 MDS codes in Hamming graphs and of the latin hypercubes. We prove the characterization of these…
On a test on switching separability of graphs modulo
Evgeny Bespalov, Denis Krotov
We consider the graphs whose edges are marked by the integers (weights) from to (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked…