Abstract
We are going to study the properties of graphs whose automorphism group acts vertex transitively. A vertex-transitive graph is necessarily regular. One challenge is to find properties of vertex-transitive graphs that are not shared by all regular graphs. We will see that transitive graphs are more strongly connected than regular graphs in general. Cayley graphs form an important class of vertex-transitive graphs; we introduce them and offer some reasons why they are important and interesting.
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