Some problems about symmetries of finite graphs

Not scheduled
15m
UP FHS (Koper)

UP FHS

Koper

Titov trg 5,Koper

Speaker

Mr Primož Potočnik (University of Ljubljana)

Description

A few topics regarding symmetries of finite graphs that I find interesting, intriguing and worth studying shall be presented.

Summary

I would like to mention a few topics regarding symmetries of finite graphs that I find interesting, intriguing and worth studying.

The first topic is about lifting automorphisms along covering projections. Suppose one is given a finite connected graph $\Gamma$ and a group of automorphisms $G$ acting on it. Can one find a regular covering projection $\wp$ onto $\Gamma$ such that $G$ is the maximal group that lifts along $\wp$ and such that the full automorphism group of the graph is the lift of $G$? A recent partial result answer proved recently my Pablo Spiga and myself will be presented.

The second topic is about vertex-transitive graphs admitting an automorphism fixing many vertices; here a strict definition of the term ``many'' is intentionally avoided so that by varying it one can prove different results. Some computational data regarding cubic vertex-transitive graphs will be presented.

If time permits, a third topic regarding vertex-transitive graphs admitting an automorphism with a long orbit will be discussed; here the term ``long'' means a suitable fixed proportion of the order of the graph. Some results obtained recently by Micael Toledo about the cubic case will be mentioned.

Primary author

Mr Primož Potočnik (University of Ljubljana)

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