arXiv subjects

Viktor A. Byzov

Publications and source records attributed to Viktor A. Byzov.

4 recordsLinked to original sources

arXiv2026

The Partition of Paley Graphs into Petersen Graphs and a New Strongly Regular Graph with Parameters (50, 21, 8, 9)

This paper utilizes an extremely simple idea: in the multiplicative group of a finite field $F_q$, cosets of a certain subgroup are considered, and an attempt is made to combine these cosets into pairs such that the resulting induced subgraph in the corresponding Paley graph is strongly regular. It is shown that there exists an infinite sequence of Paley graphs that can be partitioned into Petersen graphs in this manner. Furthermore, a new strongly regular graph with parameters $(50, 21, 8, 9)$ is constructed using this method.

math.CO↗

arXiv2026

On an infinite sequence of strongly regular digraphs with parameters $(9(2n+3), 3(2n+3), 2n+4, 2n+1, 2n+4)$

The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification operation consistent with polynomial arithmetic modulo $x^{2n+3}-1$. Using computer search with the pychoco library and subsequent analysis of automorphism groups in the GAP system, a stable structural pattern was identified, which made it possible to formulate and prove an explicit formula for the adjacency matrices of the infinite sequence of directed graphs. Among the obtained digraphs, there are examples with parameters $(63, 21, 8, 5, 8)$ and $(81, 27, 10, 7, 10)$, for which the question of existence had previously remained open. A hypothesis on the structure of the automorphism groups of the digraphs in the constructed sequence is also formulated.

math.CO↗

arXiv2025

Explicit construction of infinite families of strongly regular digraphs with parameters $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$

An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$ is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained by the constructed recurrence. Using the described approach, 11 families of strongly regular digraphs were found. In particular, these families contain digraphs $\text{dsrg}(72, 18, 5, 3, 5)$, $\text{dsrg}(76, 19, 5, 4, 5)$, $\text{dsrg}(92, 23, 6, 5, 6)$ and $\text{dsrg}(104, 26, 7, 5, 7)$, the question of the existence of which was previously open.

math.CO↗

arXiv2025

On the existence of directed strongly regular graphs with parameters (22, 9, 6, 3, 4)

The paper shows the existence of a family of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). The adjacency matrices of the found digraphs are composed of $3\times 3$ circulant blocks. The automorphism group of all the digraphs found is the group $\mathbb{Z}_3$. The structure of the resulting digraphs is described using concepts of skeleton and rigging.

math.CO↗