Graph Automorphism

A graph automorphism is a form of symmetry in graph theory in which a graph is mapped onto itself while preserving its edge-vertex connectivity, that is, a permutation of the graph's vertices under which connected pairs of vertices remain connected. The composition of two automorphisms is again an automorphism, and the full collection of a graph's automorphisms forms a group under composition called its automorphism group. By Frucht's theorem, every abstract group can be represented as the automorphism group of some connected graph, linking graph symmetry directly to general group theory.