Vertex-transitive graph

In the mathematical field of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges.

The finite Cayley graphs (such as cube-connected cycles) are also vertex-transitive, as are the vertices and edges of the Archimedean solids (though only two of these are symmetric).

Potočnik, Spiga and Verret have constructed a census of all connected cubic vertex-transitive graphs on at most 1280 vertices.

[3] The edge-connectivity of a connected vertex-transitive graph is equal to the degree d, while the vertex-connectivity will be at least 2(d + 1)/3.

[5] In 2005, Eskin, Fisher, and Whyte confirmed the counterexample.

The edges of the truncated tetrahedron form a vertex-transitive graph (also a Cayley graph ) which is not symmetric .