SEMINAR: Groups and Combinatorics Seminar 16:00 Fri 09/03/2018 Weatherburn LT: Alejandra Ramos Rivera (UWA and University of Primorska, FAMNIT, Koper, Slovenia)

Speaker: Alejandra Ramos Rivera (UWA and University of Primorska, FAMNIT, Koper, Slovenia)

Title: Structural results on tetravalent half-arc-transitive graphs

Time and place: 16:00 Friday 09/03/2018 in Weatherburn LT

Abstract: In this talk we focus on tetravalent graphs admitting a half-arc-transitive subgroup of automorphisms, that is a subgroup acting transitively on its vertices and its edges but not on its arcs. One of the most fruitful approaches for the study of structural properties of such graphs is the well known paradigm of alternating cycles and their intersections which was introduced by Marušič 20 years ago.

We introduce a new parameter for such graphs, giving a further insight into their structure. Various properties of this parameter are given. The obtained results are used to establish a link between two frameworks for a possible classification of all tetravalent graphs admitting a half-arc-transitive subgroup of automorphisms, the one proposed by Marušič and Praeger in 1999, and the much more recent one proposed by Al-bar, Al-kenai, Muthana, Praeger and Spiga which is based on the normal quotients method.

We also present results on the graph of alternating cycles of a tetravalent graph admitting a half-arc-transitive subgroup of automorphisms. A considerable step towards the complete answer to the question of whether the attachment number necessarily divides the radius in tetravalent half-arc-transitive graphs is made.

Past and future seminars may be found at http://www.maths.uwa.edu.au/~glasby/GroupsAndCombinatoricsSeminar/S18.html

There will be cake in the Mathematics and Statistics tea room at 15:40. The seminar starts at 16:00, and after 17:05 we go to the UniClub or Student Tavern for a drink.