V. Kabanov

activity

20172023

most citedOn strictly Deza graphs with parameters (n,k,k-1,a)

11 citations · 39 across the 12 of their papers we have counts for

collaborators

12 papers

math.CO2023

Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique

Alexander L. Gavrilyuk, Vladislav V. Kabanov

In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The…

math.CO2022

A new construction of strongly regular graphs with parameters of the complement symplectic graph

Vladislav V. Kabanov

The symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible desi…

math.CO2021

New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs

Vladislav V. Kabanov

A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1 ,lambda_2, m, n) if its vertex set can be partitioned into m classes of size n, such tha…

math.CO2021

Spectra of strongly Deza graphs

Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh +3

A Deza graph $G$ with parameters $(n, k, b, a)$ is a $k$ -regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_{A}$ and…

math.CO2020★ 5 cited

Generalised dual Seidel switching and Deza graphs with strongly regular children

Vladislav V. Kabanov, Elena V. Konstantinova, Leonid Shalaginov

A Deza graph G with parameters (n,k,b,a) is a k-regular graph with n vertices such that any two distinct vertices have b or a common neighbours, where b >= a. The children G_A and…

math.CO2019★ 1 cited

Minimum supports of eigenfunctions with the second largest eigenvalue of the Star graph

Vladislav Kabanov, Elena V. Konstantinova, Leonid Shalaginov +1

The Star graph $S_{n}$ , $n \geq 3$ , is the Cayley graph on the symmetric group $S y m_{n}$ generated by the set of transpositions ${(12), (13), \dots, (1 n)}$ . In this work we study eigenfu…

math.CO2019★ 4 cited

On divisible design Cayley graphs

Vladislav V. Kabanov, Leonid Shalaginov

We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.

math.CO2019★ 2 cited

Deza graphs with parameters (v,k,k-2,a)

Vladislav Kabanov, Leonid Shalaginov

A Deza graph with parameters $(v, k, b, a)$ is a $k$ -regular graph on $v$ vertices in which the number of common neighbors of two distinct vertices takes two values $a$ or $b$ ($a\leq…

math.CO2018

Deza graphs with parameters $(n, k, k - 1, a)$ and $β = 1$

Sergey Goryainov, Willem H. Haemers, Vladislav V. Kabanov +1

A Deza graph with parameters $(n, k, b, a)$ is a $k$ -regular graph with $n$ vertices in which any two vertices have $a$ or $b$ ( $a \leq b$ ) common neighbours. A Deza graph is strictly…

math.CO2018★ 6 cited

$P I$ -eigenfunctions of the Star graphs

Sergey Goryainov, Vladislav Kabanov, Elena Konstantinova +2

We consider the symmetric group $Sym_{n}, n ⩾ 2$ , generated by the set $S$ of transpositions $(1 i), 2 ⩽ i ⩽ n$ , and the Cayley graph $S_n=Cay(\math…

math.CO2018★ 10 cited

On eigenfunctions and maximal cliques of Paley graphs of square order

Sergey Goryainov, Vladislav V. Kabanov, Leonid Shalaginov +1

In this paper we find new maximal cliques of size $\frac{q + 1}{2}$ or $\frac{q + 3}{2}$ , accordingly as $q \equiv 1 (4)$ or $q \equiv 3 (4)$ , in Paley graphs of order $q^{2}$ , where $q$ is…

math.CO2017★ 11 cited

On strictly Deza graphs with parameters (n,k,k-1,a)

V. V. Kabanov, N. V. Maslova, L. V. Shalaginov

A nonempty $k$ -regular graph $Γ$ on $n$ vertices is called a Deza graph if there exist constants $b$ and $a$ $(b \geq a)$ such that any pair of distinct vertices of $Γ$ has precise…