13 papers · 1 filter
On Neumaier Cayley graphs
Rhys J. Evans, Sergey Goryainov, Grigory Ryabov +1
In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further…
Divisible design graphs from Higmanian association schemes
Grigory Ryabov
An imprimitive symmetric indecomposable association scheme of rank 5 is said to be Higmanian. A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a…
Directed strongly regular graphs and divisible design graphs from Tatra association schemes
Mikhail Muzychuk, Grigory Ryabov
In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. W…
Deza Cayley graphs from difference sets
Grigory Ryabov
In this note, we provide several constructions of Deza Cayley graphs over groups having a generalized dihedral subgroup. These constructions are based on a usage of (relative) diff…
On CI-property of normal Cayley digraphs over abelian groups
Grigory Ryabov
A Cayley digraph over a finite group is said to be CI if for every Cayley digraph over isomorphic to , there is an isomorphism from to whic…
On a family of divisible design digraphs
Mikhail Muzychuk, Grigory Ryabov
For every odd prime power , a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg grou…