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Optimized algorithm to find all symmetry-distinct maps of a graph: Application to topology-driven molecular design. (English) Zbl 1187.92085
Summary: We describe an optimized algorithm for finding all symmetry-distinct maps of a given graph. It contains significant improvements on the computing time by representing the maps as linear codes. In this way, the time consuming step of removing equivalent maps can be solved more efficiently by searching for a “minimal code”. As an example we apply the algorithm to the 32-vertex Dyck-graph for which more than 4 billion cases should be investigated. One of its most symmetrical maps forms an interesting blueprint for a hypothetical negatively curved carbon allotrope of genus 3.

MSC:
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C90 Applications of graph theory
05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
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