Vertex-transitive Graphs

Finite Transitive Graphs

A transitive graph refers to a graph whose automorphism group acts transitively on its vertex set.

In simpler terms, this means that for any two vertices u and v in the graph, there exists an automorphism (a permutation of the vertices that preserves the graph structure) that maps vertex u to vertex v. In other words, the automorphism group of a transitive graph "moves" any vertex to any other vertex in the graph while maintaining the graph structure.

0. Every vertex-transitive graph is regular. But the converse is false.

Frucht graph                                                              Tietze's graph