Realizations of crystal nets. I. (Generalized) derived graphs

A crystal net can be derived from a `generalized' voltage graph representing a graph analog of a fundamental domain of that crystal net along with a sufficient collection of its symmetries. The voltage assignments include not only isometries to the (oriented) edges, but also `weight' groups assigned to vertices for generating the vertex figures around those vertices. By varying the voltage assignments, one obtains geometrically distinct – and occasionally topologically distinct – Euclidean graphs. The focus here is on deriving simple graphs, i.e. graphs with no loops or lunes, especially uninodal edge transitive graphs.

Source: Acta Crystallographica Section A - December 19, 2023 Category: Chemistry Authors: McColm, G. Tags: crystal nets parametrization realizations of graphs voltage graphs periodic graphs research papers Source Type: research