Recursive generation of IPR fullerenes

TL;DR

This paper introduces a new recursive algorithm for generating all non-isomorphic IPR fullerenes efficiently, covering a broad class of structures and enabling enumeration up to 400 vertices.

Contribution

The authors present a novel recursive construction algorithm that stays within the class of IPR fullerenes, improving efficiency over previous methods.

Findings

Faster generation of IPR fullerenes compared to existing algorithms

Complete enumeration of IPR fullerenes up to 400 vertices

Identification of 36 irreducible IPR fullerenes and 4 nanotube families

Abstract

We describe a new construction algorithm for the recursive generation of all non-isomorphic IPR fullerenes. Unlike previous algorithms, the new algorithm stays entirely within the class of IPR fullerenes, that is: every IPR fullerene is constructed by expanding a smaller IPR fullerene unless it belongs to limited class of irreducible IPR fullerenes that can easily be made separately. The class of irreducible IPR fullerenes consists of 36 fullerenes with up to 112 vertices and 4 infinite families of nanotube fullerenes. Our implementation of this algorithm is faster than other generators for IPR fullerenes and we used it to compute all IPR fullerenes up to 400 vertices.