An automorphism of a graph G is defined as a permutation p of the vertex set such that an edge {a,b} exists if and only if the edge {p(a), p(b)} also exists. This definition aligns with the concept of isomorphism, where an automorphism is a specific type of isomorphism where the domain and codomain are the same. Therefore, an isomorphism f: G -> G is classified as an automorphism of G, confirming the relationship between these two concepts.
PREREQUISITESMathematicians, computer scientists, and students studying graph theory, particularly those interested in the properties and applications of graph automorphisms and isomorphisms.