Y. Gao, H. Zhang
Sharp upper bounds on the Clar number of fullerene graphs
Discussiones Mathematicae Graph Theory
Received 12.02.2016, Revised 26.10.2016, Accepted 26.10.2016, doi: 10.7151/dmgt.2013
The Clar number of a fullerene graph with n vertices is bounded above by ⌊ n/6⌋-2 and this bound has been improved to ⌊ n/6⌋-3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n≥20 except n=22 and n=30.
fullerene, Clar number, Clar set, leapfrog transformation