Algebra Seminar: Akpanya -- Regular Graphs with given Automorphism Groups

Reymond Akpanya (University of Sydney) will be speaking in the algebra seminar.  We will
go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday October 9 

Where: Carslaw 275 

Title: Regular Graphs with given Automorphism Groups 

Abstract: A classical theorem of Frucht states that every finite group occurs as the
automorphism group of a finite graph.  In this talk, we prove an embedded analogue for
regular graphs of every degree at least three.  In particular, for every integer
$d\geq3$ and every finite group $G$, there exists a $d$-regular graph $\Gamma$ together
with a strong embedding $\beta$ into a closed surface such that $\Aut(\Gamma)\cong
\Aut(\beta,\Gamma)\cong G$.  Along the way, we identify an oversight in Sabidussi’s
classical construction of regular graphs with prescribed automorphism groups.  We give
an alternative construction that resolves this issue and strengthens Sabidussi’s
result by producing graphs that admit proper $d$-edge-colourings preserved by every
graph automorphism.  

This is joint work with Meike Weiss (RWTH Aachen) and Tom Goertzen (University of
Sydney).