45 citations · 110 across the 16 of their papers we have counts for
16 papers
Extremal Peisert-type graphs without the strict-EKR property
Sergey Goryainov, Chi Hoi Yip
It is known that Paley graphs of square order have the strict-EKR property, that is, all maximum cliques are canonical cliques. Peisert-type graphs are natural generalizations of P…
Equitable 2-partitions of the Johnson graphs
Rhys J. Evans, Alexander L. Gavrilyuk, Sergey Goryainov +1
We finish the classification of equitable 2-partitions of the Johnson graphs of diameter 3, , for .
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 \…
The EKR-module property of pseudo-Paley graphs of square order
Shamil Asgarli, Sergey Goryainov, Huiqiu Lin +1
We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdős-Ko-Rado (EKR) module property, in a sense that the char…
A general construction of strictly Neumaier graphs and a related switching
Rhys J. Evans, Sergey Goryainov, Elena V. Konstantinova +1
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show th…
On balanced characteristic functions of canonical cliques in Paley graphs of square order
Sergey Goryainov, Huiqiu Lin
In this paper we prove that balanced characteristic functions of canonical cliques in a Paley graph of square order span the -eigenspace of the graph. This…
The spanning -trees, perfect matchings and spectral radius of graphs
Dandan Fan, Sergey Goryainov, Xueyi Huang +1
A -tree is a spanning tree in which every vertex has degree at most . In this paper, we provide a sufficient condition for the existence of a -tree in a connected graph wi…
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…
Integral graphs obtained by dual Seidel switching
Sergey Goryainov, Elena V. Konstantinova, Honghai Li +1
Dual Seidel switching is a graph operation introduced by W.~Haemers in 1984. This operation can change the graph, however it does not change its bipartite double, and because of th…
The smallest strictly Neumaier graph and its generalisations
Rhys J. Evans, Sergey Goryainov, Dmitry Panasenko
A regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the…
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…
Equitable partitions of Latin-square graphs
R. A. Bailey, Peter J. Cameron, Alexander L. Gavrilyuk +1
We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue .
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…