Faculty of Mathematics, Physics
and Informatics
Comenius University in Bratislava

Algebraic Graph Theory Seminar- Ted Dobson (11.2.2019)

Monday 11.2.2019 at 10:00, Lecture roon M/213


06. 02. 2019 15.11 hod.
By: Martin Mačaj

I would like to invite you to the joint lecture of Graph Theory Seminar and Algebraic Graph Theory Seminar


Ted Dobson
(University of Primorska): 
On Automorphisms of Haar graphs of Abelian Groups


Abstract:
Let G be a group and S ⊆ G. A Haar graph of G with connection set S has vertex set Z2 × G and edge set {(0; g)(1; gs) : g ∈ G and s ∈ S}. Haar graphs are then natural bipartite analogues of Cayley digraphs. We rst examine the relationship between the automorphism group of a Cayley digraph of G with connection set S and a Haar graph of G with connection set S. We establish that the automorphism group of a Haar graph contains a natural subgroup isomorphic to the automorphism group of the corresponding Cayley digraph. In the case where G is abelian, we then give four situations in which the automorphism group of the Haar graph can be larger than the natural subgroup corresponding to the automorphism group of the Cayley digraph together with a speci c involution, and analyze the full automorphism group in each of these cases. As an application, we show that all s-transitive Cayley graphs of generalized dihedral groups have a quasiprimitive automorphism group, can be \reduced" to s-arc-transitive graphs of smaller order, or are Haar graphs of abelian groups whose automorphism groups have a particular permutation group theoretic property.