Asymptotic enumeration of perfect matchings in m -barrel fullerene graphs
Résumé
A connected planar cubic graph is called an m-barrel fullerene and denoted by F(m,k), if it has the following structure: The first circle is an m-gon. Then m-gon is bounded by m pentagons. After that we have additional k layers of hexagons. At the last circle m-pentagons connected to the second m-gon. In this paper we asymptotically count by two different methods the number of perfect matchings in m-barrel fullerene graphs, as the number of hexagonal layers is large, and show that the results are equal.
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