S. Goryainov

Erdős-Ko-Rado properties of Steiner 2-designs

Sam Adriaensen, Sergey Goryainov, Elena V. Konstantinova +1

In this paper, we prove an Erdős-Ko-Rado characterisation of maximum intersecting families of blocks in Steiner $2$ -designs arising from Desarguesian maximal arcs. This answers a r…

Divisible design graphs obtained by plugging a difference set into a construction for antipodal distance-regular graphs of diameter 3

Bart De Bruyn, Sergey Goryainov, Ruilin Ma +1

In this paper, we present a new construction of divisible design graphs with new parameters, obtained by plugging a difference set of a quotient group into a known construction of…

A family of Neumaier graphs containing examples with exactly five eigenvalues

Bart De Bruyn, Rhys J. Evans, Sergey Goryainov +1

A Neumaier graph is an edge-regular graph with a regular clique. Such a graph is said to have parameters $(v, k, λ; e, s)$ if it is a $k$ -regular graph on $v$ vertices having a clique…

On Neumaier Cayley graphs

Rhys J. Evans, Sergey Goryainov, Grigory Ryabov +1

In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further…

Thin divisible designs graphs: an interplay between fixed-point free involutions of $(v, k, λ)$ -graphs and symmetric weighing matrices

Sergey Goryainov, Willem H. Haemers, Elena V. Konstantinova +1

In this paper, we illustrate important aspects of the interplay between weighing matrices, $(v, k, λ)$ -graphs with fixed-point free involutions, and signed graphs with an orthogonal…

The spectral Turán problem: Characterizing spectral-consistent graphs

Longfei Fang, Sergey Goryainov, Denis Krotov +2

Let $EX (n, H)$ and $SPEX (n, H)$ denote the families of $n$ -vertex $H$ -free graphs with the maximum size and the maximum spectral radius, respectively. A graph $H$ is said…

Divisible design graphs with selfloops

Anwita Bhowmik, Bart De Bruyn, Sergey Goryainov

We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical…

Cliques in Paley graphs of square order and in Peisert graphs

Andries E. Brouwer, Sergey Goryainov, Leonid Shalaginov +1

We study maximal cliques in the collinearity graphs of Desarguesian nets, give some structural results and some numerical information. In particular, we show for Desarguesian nets…

Divisible design graphs from symplectic graphs over rings with precisely three ideals

Anwita Bhowmik, Sergey Goryainov

In this paper we construct two new infinite families of divisible design graphs based on symplectic graphs over rings with precisely three ideals.

math.CO2024★ 1 cited

Completely regular codes in graphs covered by a Hamming graph

Sergey Goryainov, Denis Krotov

In Cayley graphs on the additive group of a small vector space over GF $(q)$ , $q = 2, 3$ , we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the…

Second largest maximal cliques in small Paley graphs of square order

Huye Chen, Sergey Goryainov, Cong Hu

There is a conjecture that the second largest maximal cliques in Paley graphs of square order $P (q^{2})$ have size $\frac{q + ε}{2}$ , where $q \equiv ε (mod 4)$ , and split into two orbi…

Tightness of the weight-distribution bound for strongly regular polar graphs

Rhys J. Evans, Sergey Goryainov, Leonid Shalaginov

In this paper we show the tightness of the weight-distribution bound for the positive non-principle eigenvalue of strongly regular (affine) polar graphs and characterise the optima…