Description
A combinatorial d-dimensional zeolite is the line graph of a (d+1)-regular graph. We show that not all combinatorial 2-d zeolites have a unit distance realization in the plane, and of those that have a unit distance realization, not all have non-overlapping unit-distance realizations. Only few classes of finite 2-d zeolites are known and a long standing conjecture of Harborth suggests that there is only one type of non-overlapping unit distance realizable finite 2-d zeolites. However, for all d geater than 1, we prove that there are uncountably many distinct infinite non-overlapping unit distance realizable zeolites. Infinite 3-d zeolites are the objects of interest to Chemists and Physicists and have important industrial applications.
Primary author
Prof.
Brigitte Servatius
(Worcester Polytechnic Institute)
