8th Croatian Mathematical Congress

Directed regular graphs from groups

2 Jul 2024, 16:05

20m

D3 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Talk CDM: Combinatorics and Discrete Mathematics Combinatorics and Discrete Mathematics

Speaker

Matea Zubović Žutolija (Faculty of Mathematics, University of Rijeka)

Description

Regular directed graph $\mathrm{\Gamma }$ of degree $k$ with $n$ vertices is directed strongly regular graph, $DSRG(n,k,\lambda ,\mu ,t)$, if number of directed paths of length two from every vertex $v$ to every vertex $w$ is $\lambda$ if there exists directed edge $v\to w$, $t$ if $v=w$ and $\mu$ if there is no edge $v\to w$. Directed strongly regular graphs were introduced by Art Duval in 1988.
One can construct 1-design by defining a basic block as union of $G_{\alpha }$-orbits of transitive permutation group. Using that, we construct directed regular and strongly regular graphs from transitive groups.