Algebraic Graph Theory Seminar - Štefan Gyürki (29.11.2019)

Friday 29.11.2019 at 13:30, Lecture room XI

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Štefan Gyürki (Slovak University of Technology):
Constructions of Directed Strongly Regular Graphs Using Computer Algebra

Abstract:
Central objects of the talk are directed strongly regular graphs, which are one of the possible generalizations of classical (undirected) strongly regular graphs playing important role in Algebraic Graph Theory. A \emph{directed strongly regular graph} (DSRG, for short) with parameters $(n,k,t,\lambda,\mu)$ is a regular mixed graph on~$n$ vertices with valency $k$ such that every vertex is incident with~$t$ undirected edges; the number of directed paths of length 2 directed from a vertex $x$ to another vertex $y$ is~$\lambda$, if there is an arc from $x$ to~$y$ and $\mu$ otherwise. In the talk we show a few constructions of DSRGs, which originate as results of careful computer analysis of known single DSRGs, their interpretation on combinatorial and theoretical level, and finally their succesful generalization. We show constructions of DSRGs which are related to other combinatorial structures including association schemes, equitable partitions and Latin squares.

 

 

 

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