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- Institute for Theoretical and Experimental PhysicsRU30 papers
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20 papers · 1 filter
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…
On eigenfunctions of the block graphs of geometric Steiner systems
Sergey Goryainov, Dmitry Panasenko
This paper lies in the context of the studies of eigenfunctions of graphs having minimum cardinality of support. One of the tools is the weight-distribution bound, a lower bound on…
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 \…
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…
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…
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…