Abstract
A graph $$\Gamma$$ is called homogenous if the group of automorphisms of $$\Gamma$$ acts transitively on the set of vertices of $$\Gamma$$ . We will study the following properties for homogenous graphs: Removability: a vertex p is removable if the graph obtained by removing it is isomorphic to the original. Property (R): for every edge x there exists an edge y such that removing x and y disconnects the graph. We will study also Cayley graphs of groups of automorphisms of graphs with the property (R) and related concepts.
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