Chirality for simple graphs of size up to 12
Howon Choi, Hyoungjun Kim, Sungjong No

TL;DR
This paper classifies minor minimal intrinsically chiral simple graphs with up to twelve vertices, advancing understanding of molecular chirality through graph theory.
Contribution
It provides a complete classification of minor minimal intrinsically chiral graphs for simple graphs of size up to twelve, linking graph theory to molecular chirality.
Findings
Identified all minor minimal intrinsically chiral graphs up to 12 vertices.
Established a finite set of such graphs based on Robertson and Seymour's theorem.
Enhanced understanding of chirality in molecular structures via graph classification.
Abstract
Chirality is one of the important assymmetrical property in wide area of natural science, which has been studied to predict molecular behavior. One of good methods to analyze molecules with complex structures is representing them as graphs embedded in 3-dimensional space. So it is important to study the chirality of spatial graphs to understand structure of chiral molecules. Moreover, Robertson and Seymour's graph minor theorem implies that a set of minor minimal graphs with respect to intrinsic properties is finite. So it is also important to find a complete set of minor minimal graphs for intrinsic properties. In this paper, we classify minor minimal intrinsically chiral graphs among simple graphs of size up to twelve.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications · Surface Chemistry and Catalysis · Supramolecular Self-Assembly in Materials
