At least half of the leapfrog fullerene graphs have exponentially many Hamilton cycles

A fullerene graph is a 3‐connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the dual of the truncation of the given graph. A fullerene graph is a leapfrog if it can be obtained from another fullerene graph by the leapfrog transformation. We prove that leapfrog fullerene graphs on n = 12 k − 6 vertices have at least 2 k Hamilton cycles.