Chirality for simple graphs of size up to 12

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.