arXiv subjects

Štefan Gyürki

Publications and source records attributed to Štefan Gyürki.

5 recordsLinked to original sources

arXiv2026

An infinite family of intransitive directed strongly regular graphs with rank 6 Weisfeiler--Leman closure

We construct an infinite family of directed strongly regular graphs (DSRGs) with intransitive full automorphism groups whose Weisfeiler--Leman closure are association schemes of rank 6. This is the smallest possible rank for an association scheme admitting a proper DSRG merging. We also exhibit rigid sporadic DSRGs with the same closure property, showing that combinatorial regularity, group-theoretic symmetry, and Weisfeiler--Leman regularity capture fundamentally different aspects of graph structure.

math.CO↗

arXiv2026

Directed strongly regular graphs from groups, loops and quasigroups

We introduce four infinite families of directed strongly regular graphs of orders $2n^2$ and $3n^2$. The constructions are described in terms of groups, quasigroups, loops and their Latin squares. Two preliminary Cayley digraph constructions over wreath products are extended to arbitrary quasigroups and loops, yielding directed strongly regular graphs with parameters $(2n^2,3n-2,2n-1,n-1,3),(2n^2,4n-2,2n+2,n+2,6),(3n^2,4n-2,2n,n,4),(3n^2,6n-2,2n+6,n+6,10)$.

math.CO↗

arXiv2015

Construction of infinite families of non-Schurian association schemes of order $2p^2$, $p$ an odd prime, based on biaffine planes and Heisenberg groups: research report and beyond

Let $p$ be an odd prime. In this paper we provide a construction which gives four non-Schurian association schemes for every $p\geq 5$ and two for $p=3$. This construction is explained using incidences between points and lines of a biaffine plane and we also provide a pure algebraic model for it with the aid of finite Heisenberg groups. The obtained results are discussed in a more wide framework.

math.CO↗

arXiv2015

New infinite families of directed strongly regular graphs via equitable partitions

In this paper we introduce a construction of directed strongly regular graphs from smaller ones using equitable partitions. Each equitable partition of a single DSRG satisfying several conditions leads to an infinite family of directed strongly regular graphs. We construct in this way dozens of infinite families. For order at most 110, we confirm the existence of DSRGs for 30 previously open parameter sets.

math.CO↗

arXiv2014

Sporadic Examples of Directed Strongly Regular Graphs Obtained by Computer Algebra Experimentation (Extended version)

We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley graphs over non-Abelian groups. We demonstrate examples of directed strongly regular graphs for 28 different parameter sets, for which the existence of a corresponding digraph has not been known before.

math.CO↗