Raziskovalni matematični seminar
Raziskovalni matematični seminar poteka v organizaciji oddelkov za matematiko dveh članic Univerze na Primorskem - UP FAMNIT in Inštituta Andrej Marušič (UP IAM), in sicer vsak ponedeljek od oktobra do junija.
Vljudno vabljeni k udeležbi na prihodnjih seminarjih!
Datum in ura / Date and time: 27.2.24
(14:00 -- 15:00)
Predavalnica / Location: FAMNIT-VP1
Predavatelj / Lecturer: Joy Morris (University of Lethbridge, Canada)
Naslov / Title: Detecting (Di)Graphical Regular Representations
Vsebina / Abstract:
Graphical and Digraphical Regular Representations (GRRs and DRRs) are a concrete way to visualise the regular action of a group, using (di)graphs. More precisely, a GRR or DRR on the group $G$ is a (di)graph whose automorphism group is isomorphic to the regular action of $G$ on itself by right-multiplication.
For a (di)graph to be a DRR or GRR on $G$, it must be a Cayley (di)graph on $G$. Whenever the group $G$ admits an automorphism that fixes the connection set of the Cayley (di)graph setwise, this induces a nontrivial graph automorphism that fixes the identity vertex, which means that the (di)graph is not a DRR or GRR. Checking whether or not there is any group automorphism that fixes a particular connection set can be done very quickly and easily compared with checking whether or not any nontrivial graph automorphism fixes some vertex, so it would be nice to know if there are circumstances under which the simpler test is enough to guarantee whether or not the Cayley graph is a GRR or DRR. I will present a number of results on this question.
Join Zoom Meeting
https://upr-si.zoom.us/j/85914318577
Meeting ID: 859 1431 8577
Don't miss out on this opportunity to delve into cutting-edge research and expand your mathematical horizons!
