engleski

Empirical study of diameters in fullerene graphs

We have computed the diameters of all fullerene graphs on $20 \leq n \leq 120$ vertices and of all fullerene graphs with isolated pentagons on $60 \leq n \leq 146$ vertices. The results are used to asses the quality of recently obtained linear upper bounds and sqare root-type lower bounds. It seems that the fullerenes with large diameters are exceedingly rare. Our results suggest that there is a linear upper bound on the diamater of the fullerenes with isolated pentagons and that the minimum diameter is achieved on an isomer with isolated pentagons for large enough number of vertices.

Fullerene graph; Diameter

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