Abstract
A fullerene graph is a three-regular and three-connected plane graph exactly 12 faces of which are pentagons and the remaining faces are hexagons. Let F n be a fullerene graph with n vertices. The Clar number c(F n ) of F n is the maximum size of sextet patterns, the sets of disjoint hexagons which are all M-alternating for a perfect matching (or Kekule structure) M of F n . A sharp upper bound of Clar number for any fullerene graphs is obtained in this article: $$c(F_n)\leqslant \lfloor \frac {n-12} 6\rfloor$$ . Two famous members of fullerenes C60 (Buckministerfullerene) and C70 achieve this upper bound. There exist infinitely many fullerene graphs achieving this upper bound among zigzag and armchair carbon nanotubes.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
