The Crystal Net Isomorphism Problem.

25^th November 2024, 14:00
Gregory McColm
University of South Florida, USA

Abstract

A covalent crystal may be represented as a graph, with atoms or molecular building blocks as vertices and bonds as edges. Such a graph can be called a crystal net, a crystal structure, or a periodic graph. Two such graphs are often regarded as equivalent if they are isomorphic, so isomorphism is critical to many modern cataloguing systems. While isomorphism is readily established for certain nice classes of crystal nets, the general case is at least as hard as the (finite) Graph Isomorphism Problem, for when no fast algorithm is known. We look at the Crystal Net Isomorphism Problem from the point of view of voltage graphs.