School of Mathematics and Statistics

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Cores of vertex-transitive graphs

Rotheram, Ricky ( 2013)

The core of a graph $\Gamma$ is the smallest graph $\Gamma^\ast$ for which there exist graph homomorphisms $\Gamma\rightarrow\Gamma^\ast$ and $\Gamma^\ast\rightarrow\Gamma$. Thus cores are fundamental to our understanding of general graph homomorphisms. It is known that for a vertex-transitive graph $\Gamma$, $\Gamma^\ast$ is vertex-transitive, and that $\left|V(\Gamma^\ast)\right|$ divides $\left|V(\Gamma)\right|$. The purpose of this thesis is to determine the cores of various families of vertex-transitive and symmetric graphs. We focus primarily on finding the cores of imprimitive symmetric graphs of order $pq$, where $p
Adolescent perceptions of the concept of randomness

Toohey, Phillip Gerard ( 1994)

An investigation into adolescents perceptions of concepts of randomness, with a questionnaire trialled on 75 adolescent boys between Year 7 and Year 11 in Catholic schools in Melbourne, Australia.
Duality groups

AISBETT, NATALIE ( 2011)

This thesis focuses mainly on the subclass of complex reflection groups called duality groups. We have worked towards a new classification of the duality groups. As well as this, an analysis of affine diagrams has been done to set the framework for the possibility of defining a new class of groups, affine duality groups defined analogously to affine Weyl groups. We have studied one family of affine duality groups.