The best constant of discrete Sobolev inequality on 1812 C60 fullerene isomers

Abstract

The best constants of discrete Sobolev inequalities corresponding to 1812 isomers of C60 fullerene are found. Classical mechanical models of these isomers with a linear spring on each edge are investigated. The best constants stand for rigidities of these models. We show the best constants of 1812 isomers are distinct rational numbers and among these, Buckyball (or equivalently truncated icosahedron) takes the least. In other words, one can say that the Buckyball is the most rigid among 1812 C60 fullerene isomers.