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SUMMARY:Joy Morris (University of Lethbridge)
DTSTART:20231031T200000Z
DTEND:20231031T210000Z
DTSTAMP:20260423T021136Z
UID:NTC/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/31/">Eas
 y Detection of (Di)Graphical Regular Representations</a>\nby Joy Morris (U
 niversity of Lethbridge) as part of Lethbridge number theory and combinato
 rics seminar\n\nLecture held in University of Lethbridge: M1060 (Markin Ha
 ll).\n\nAbstract\nGraphical and Digraphical Regular Representations (GRRs 
 and DRRs) are a concrete way to visualise the regular action of a group\, 
 using graphs. More precisely\, a GRR or DRR on the group $G$ is a (di)grap
 h whose automorphism group is isomorphic to the regular action of $G$ on i
 tself by right-multiplication.\n\nFor 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 setwis
 e\, this induces a nontrivial graph automorphism that fixes the identity v
 ertex\, which means that the (di)graph is not a DRR or GRR. Checking wheth
 er or not there is any group automorphism that fixes a particular connecti
 on set can be done very quickly and easily compared with checking whether 
 or not any nontrivial graph automorphism fixes some vertex\, so it would b
 e 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 wil
 l present a number of results on this question.\n\nThis is based on joint 
 work with Dave Morris and with Gabriel Verret.\n
LOCATION:https://researchseminars.org/talk/NTC/31/
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