Computing the Clar number of nanotubes and other fullerenes

We exhibit a polynomial time algorithm that computes the clar number of any nanotube. this algorithm can be easily extended to one that computes the clar number of fullerenes whose pentagon-clusters are all of even size. computing the clar number of planar graphs is nphard. however, it is not known if computing the clar number of fullerenes is a tractable problem. we show that the latter problem can be suitably approximated in polynomial time. we also discuss the existence of fpt-algorithms for this important problem of cheminformatics.