Abstract
A fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons. The Clar number of a fullerene is the maximum size of sextet patterns, the sets of disjoint hexagons which are all M-alternating for a Kekule structure M of F. An exact formula of Clar number of some fullerene graphs and a class of carbon nanocones are obtained in this paper.
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