On the anti-Kekulé number of leapfrog fullerenes

摘要

The Anti-Kekulé number of a connected graph G is the smallest number of edges that have to be removed from G in such way that G remains connected but it has no Kekulé structures. In this paper it is proved that the Anti-Kekulé number of all fullerenes is either 3 or 4 and that for each leapfrog fullerene the Anti-Kekulé number can be established by observing finite number of cases not depending on the size of the fullerene.