On the sextet polynomial of fullerenes

Jean-Sébastien Sereni (1, 2) , Matej Stehlík (3)

1 KAM - Department of Applied Mathematics (KAM)
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 G-SCOP_OC - Optimisation Combinatoire

We show that the sextet pattern count of every fullerene is strictly smaller than the Kekulé structure count. This proves a conjecture of Zhang and He [J Math Chem 38(3):315-324 (2005)].

Mots clés: Kekulé count; Perfect matchings; Resonant pattern; Sextet polynomial; Fullerenes

Domaines: Mathématique discrète [cs.DM]; Chimie théorique et/ou physique

Jean-Sébastien Sereni, Matej Stehlík. On the sextet polynomial of fullerenes. Journal of Mathematical Chemistry, 2010, 47 (3), pp.1121--1128. ⟨hal-00487101⟩