# Symmetric graphs and domination in graphs

#### by Guangjun Xu

Institution: Mathematics and Statistics Dept, The University of Melbourne
Date: Tue 23rd June 2009
Time: 2:15 PM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: A finite graph $\Gamma$ is said to be $G$-symmetric if $\Gamma$ admits $G$ as a group of automorphisms such that $G$ acts transitively on the ordered pairs of adjacent vertices of $\Gamma$.
In most cases, $G$ acts imprimitively on the vertices of $\Gamma$, and we call such graphs imprimitive $G$-symmetric graphs.

In this talk, I will introduce the geometric approach proposed by Gardiner and Praeger in 1995 for studying imprimitive symmetric graphs. According to this approach, three configurations can be associated with $(\Gamma, {\cal B})$, where ${\cal B}$ a nontrivial $G$-invariant partition of the vertex set of $\Gamma$.

I will survey some known results on imprimitive symmetric graphs obtained by using Gardiner and Praeger's approach.
And present our results to one open question proposed recently.