SEMINAR: Groups and Combinatorics Seminar


Groups and Combinatorics Seminar
There will be three 25 minute talks on Tuesday 14th of June in MLR2 starting at 10:30 am.
10:30am:
Sylvia Ozols (Adelaide)
will speak on
The BruckBose Construction
11am:
Wei Jin (UWA)
will speak
On distance, geodesic and arc transitivity of graphs
11:30am
Carmen Amarra (UWA)
will speak on
Quotientcomplete arctransitive graphs
Abstract 1:
The BruckBose representation of a projective plane is a tool both for examining objects of any even dimensional projective space in the more familiar setting of a projective plane, and for 'magnifying' objects in certain projective planes by looking at them in a higher dimensional space. In this talk we will go through some finite projective geometry background, including Baer subplanes and partitions of odd dimensional projective spaces. We will define the BruckBose construction and get a general understanding of how it works.
Abstract 2:
We compare three transitivity properties of finite graphs, namely, for a positive integer s, sdistance transitivity, sgeodesic transitivity and sarc transitivity. It is known that if a finite graph is sarc transitive but not (s+1)arc transitive then s<8 and s not equal to 6. We show that there are infinitely many geodesic transitive graphs with this property for each of these values of s, and that these graphs can have arbitrarily large diameter if and only if 0< s<4. Moreover, for a prime p we prove that there exists a graph of valency p that is 2geodesic transitive but not 2arc transitive if and only if p = 1 (mod 4), and for each such prime there is a unique graph with this property: it is an antipodal double cover of the complete graph K_{p+1} and is geodesic transitive with automorphism group PSL(2,p) x Z_2. This is joint work with A. Devillers, C.H. Li and C. E. Praeger.
Abstract 3:
A graph Gamma is Gquotientcomplete (for some G in Aut(Gamma)) if it has at least one nontrivial Gnormal quotient which is a complete graph, and each of its other nontrivial Gnormal quotients is either a complete graph or an empty graph. We define the parameter k to be the number of Gnormal quotients of Gamma which are complete, and in this talk we consider the family of quotientcomplete graphs with k>2. We construct all the graphs Gamma; in this family together with the corresponding automorphism groups G, and give upper bounds for k in terms of the order of Gamma.
Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 14 Jun 2011 10:30

End 
Tue, 14 Jun 2011 12:00

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Thu, 09 Jun 2011 08:09

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