The Clar and Fries Structures of a Fullerene

Elizabeth Hartung
Massachusetts College of Liberal Arts

Jack Graver
Syracuse University



Content: The Fries and Clar number of a fullerene are two parameters related to the stability of the molecule. We introduce ``Fries chains," a decomposition of the edges of a Kekule structure (or perfect matching) of a fullerene. Chains allow us to better understand the structure of these graphs and to find the Fries number for classes of fullerenes. The relationship to the Clar number and Clar chains will be discussed, and we will give a class of fullerenes with the property that the set of benzene rings (alternating hexagons) of its Clar structure and the set of benzene rings of its Fries structure are practically disjoint.

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