An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is isomorphic with G. The set of automorphisms defines a permutation group known as the graph's automorphism group. For every group Γ, there exists a graph whose automorphism group is isomorphic to Γ. The automorphism groups of a graph characterize its symmetries, and are therefore very useful in determining certain of its properties.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.