The Lower Bound of Kekule Count of Fullerenes

A fullerene graph is a planar cubic graph with only pentagonal and hexagonal faces. It has been proved that fullerene graphs have exponentially many perfect matchings. The lower bound for this number has been studied in the last 20 years. The best known result is 2(n-380/61), which is given in [13] by using the four color theorem. We generalize the structure using in [13] and obtain the improved lower bound 2(n-1820/47.29).