engleski

Spectral Properties of Fullerene Graphs

We use a result from the theory of geometric representation of graphs to show that the separator of a fullerene graph on $n$ vertices cannot exceed $24/n$, thus improving the best currently known upper bound of $1 - 3/n$. The result is then combined with a recently established upper bound on the smallest eigenvalue of fullerene graphs to show that there are only finitely many Ramanujan fullerenes. That settles down a conjecture on fullerenes made by the {; ; \em Graffiti}; ; software.

Fullerene graph; separator; ramafullerene

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