ABSTRACT
Most graphs are asymmetric; that is, the identity mapping is their only automorphism. We could also call them rigid. Well-known graphs such as hypercubes, complete graphs, complete bipartite graphs, the Petersen graph, stars, and lattices admit nontrivial automorphisms. Some other classes, such as Cayley graphs, are even defined via group actions. To understand them, it is essential to understand their symmetries. Sometimes we may even look for methods to break them. Who does not know the problem of where to place nails in order to stop a wooden structure from shifting in undesirable ways? It helps to have insight into the structure to solve this problem intelligently.
