School of Mathematics and Statistics - Theses

Permanent URI for this collection

Now showing 1 - 1 of 1

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