English

Fullerene graphs of small diameter

Combinatorics 2017-09-22 v1

Abstract

A fullerene graph is a cubic bridgeless plane graph with only pentagonal and hexagonal faces. We exhibit an infinite family of fullerene graphs of diameter 4n/3\sqrt{4n/3}, where nn is the number of vertices. This disproves a conjecture of Andova and \v{S}krekovski [MATCH Commun. Math. Comput. Chem. 70 (2013) 205-220], who conjectured that every fullerene graph on nn vertices has diameter at least 5n/31\lfloor \sqrt{5n/3}\rfloor-1.

Keywords

Cite

@article{arxiv.1604.01934,
  title  = {Fullerene graphs of small diameter},
  author = {Diego Nicodemos and Matěj Stehlík},
  journal= {arXiv preprint arXiv:1604.01934},
  year   = {2017}
}
R2 v1 2026-06-22T13:27:17.713Z