The truncation of a cage graph

摘要

The modern nanotechnology applies various cage molecules having a polyhedral shape. Topologically, a polyhedron is represented by its map. Since such a map is a plane graph, one may apply various graph-theoretical methods also for studying polyhedra. Of similar use are molecular (multi)tori. The surface of a multitorus is locally plane and allows one to apply much the same mathematical methods. This text is an introduction into the spectral theory of truncated cage graphs and truncated multitori. It anticipates further extensions.