Graph Theory Questions Medium
The graph automorphism problem in graph theory refers to the task of determining whether a given graph has any non-trivial automorphisms. An automorphism of a graph is a permutation of its vertices that preserves the adjacency relationships between them. In other words, if two vertices are adjacent in the original graph, their images under the automorphism must also be adjacent in the permuted graph.
The graph automorphism problem can be stated as follows: Given a graph G, does there exist a non-identity permutation of its vertices that preserves the adjacency relationships? In other words, can we find a permutation of the vertices that leaves the graph unchanged?
Solving the graph automorphism problem is a challenging task, and it has important applications in various fields such as computer science, chemistry, and social network analysis. It is closely related to other problems in graph theory, such as graph isomorphism and graph symmetry.