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Determining Isomorphic Crystal Structures
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DOI：10.1007/978-3-032-15641-9_19.png)
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Abstract
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A common representation of crystal structures is by periodic graphs, i.e., graphs whose automorphism groups have subgroups of translational symmetries. Such graphs may be represented as (finite) quotient graphs (called voltage graphs) whose edges are labeled by corresponding elements of their translational subgroup. We outline a polynomial time algorithm for determining whether two finite bi-deterministically edge-labeled voltage graphs with voltages from corresponding translational subgroups generate isomorphic periodic graphs. This algorithm aids in the classification of crystal structures and provides a method for determining whether two sets of building blocks can assemble isomorphic crystals.
Keywords:
Periodic Graphs
Isomorphic crystal structures
voltage graphs
graph coverings
bi-deterministic edge labeling
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