11 citations · 63 across the 18 of their papers we have counts for
19 papers
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…
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…
Divisible design graphs from the symplectic graph
Bart De Bruyn, Sergey Goryainov, Willem Haemers +1
A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization…
On eigenfunctions and maximal cliques of generalised Paley graphs of square order
Sergey Goryainov, Leonid Shalaginov, Chi Hoi Yip
Let GP be the -Paley graph defined on the finite field with order . We study eigenfunctions and maximal cliques in generalised Paley graphs GP, where $m \…
On WL-rank and WL-dimension of some Deza dihedrants
Grigory Ryabov, Leonid Shalaginov
The WL-rank of a graph is defined to be the rank of the coherent configuration of . The WL-dimension of is defined to be the smallest positive integer for which …
Classification of divisible design graphs with at most 39 vertices
Dmitry Panasenko, Leonid Shalaginov
A -regular graph is called a divisible design graph (DDG for short) if its vertex set can be partitioned into classes of size , such that two distinct vertices from the s…
Divisible design graphs with parameters and
Leonid Shalaginov
A -regular graph is called a divisible design graph (DDG for short) if its vertex set can be partitioned into classes of size , such that two distinct vertices from the s…
Deza graphs: a survey and new results
Sergey Goryainov, Leonid V. Shalaginov
In this paper we survey existing results on Deza graphs and give some new results. We present an introduction to Deza graphs for the reader who is unfamiliar with the subject, and…
Enumeration of strictly Deza graphs with at most 21 vertices
Sergey Goryainov, Dmitry Panasenko, Leonid Shalaginov
A Deza graph with parameters is a -regular graph with vertices such that any two distinct vertices have or common neighbours, where . A Deza…
On a correspondence between maximal cliques in Paley graphs of square order
Sergey Goryainov, Alexander Masley, Leonid Shalaginov
Let be an odd prime power. Denote by the value of modulo 4. In this paper, we establish a linear fractional correspondence between two types of maximal cliques of si…
Spectra of strongly Deza graphs
Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh +3
A Deza graph with parameters is a -regular graph with vertices such that any two distinct vertices have or common neighbours. The children and…
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…
Minimum supports of eigenfunctions with the second largest eigenvalue of the Star graph
Vladislav Kabanov, Elena V. Konstantinova, Leonid Shalaginov +1
The Star graph , , is the Cayley graph on the symmetric group generated by the set of transpositions . In this work we study eigenfu…
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.
Deza graphs with parameters (v,k,k-2,a)
Vladislav Kabanov, Leonid Shalaginov
A Deza graph with parameters is a -regular graph on vertices in which the number of common neighbors of two distinct vertices takes two values or ($a\leq…
Deza graphs with parameters and
Sergey Goryainov, Willem H. Haemers, Vladislav V. Kabanov +1
A Deza graph with parameters is a -regular graph with vertices in which any two vertices have or () common neighbours. A Deza graph is strictly…
-eigenfunctions of the Star graphs
Sergey Goryainov, Vladislav Kabanov, Elena Konstantinova +2
We consider the symmetric group , generated by the set of transpositions , and the Cayley graph $S_n=Cay(\math…
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 or , accordingly as or , in Paley graphs of order , where is…
On strictly Deza graphs with parameters (n,k,k-1,a)
V. V. Kabanov, N. V. Maslova, L. V. Shalaginov
A nonempty -regular graph on vertices is called a Deza graph if there exist constants and such that any pair of distinct vertices of has precise…