7 papers
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…
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…
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…