Minimal Cayley Graphs of Crystallographic Groups

Аннотация

The Cayley graphs of crystallographic groups \(G_{p}^{p}\), constructed on the minimal number of generators, are discussed. Some theorems on the existence of minimal nets, homeomorphic to such graphs, are proven. The Cayley graphs of planar and Fedorov groups, related to the arrangement of molecular crystals, are considered in detail.