On Cayley graphs of crystallographical space groups
by
Juliana Grell
Berlin

Let G be a space group, H a finite subset of symmetry operations from G and consider the Cayley graph Cay(G, H) with vertices g and edges (g, hg) for all g from G and h from H.
If H is a set of generators of G, then Cay(G, H) is connected and there is a finite set of fundamental cycles generating the whole infinite graph Cay(G, H).
We have found an algorithm deciding whether an arbitrary given finite walk is a period of an infinite periodic path of Cay(G, H) or not.
The origin of this research is a practical crystallographical problem dealing with the description and comparison of hydrogen bonded molecule structures by finite local patterns - called graph sets in chemistry. In particular, this method is applied to substances which crystallize in several polymorphs being of great interest e.g. in pharma industries.
References.
J. Grell, J. Bernstein, G. Tinhofer:
Investigation of hydrogen bond patterns: The graph set approach. Part I: General ideas and their application to structures with exactly one molecule in the asymmetric unit, Techn. Univ. München, Fak. f. Math., Report TUM M9910 (1999), submitted for publication and
Graph set analysis of hydrogen bond patterns. Some mathematical concepts, Acta. Cryst. B55 1030-1043 (1999) (URL given below)

http://journals.iucr.org/b/issues/1999/06/00/issconts.html

Date received: April 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-17.