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

Kardoš František | Zendy; Mockovčiaková Martina | Zendy

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

Author(s) -

Kardoš František,

Mockovčiaková Martina

Publication year - 2021

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22660

Subject(s) - fullerene , planar graph , combinatorics , hexagonal crystal system , mathematics , graph , cubic graph , outerplanar graph , planar , line graph , discrete mathematics , voltage graph , computer science , physics , chemistry , crystallography , quantum mechanics , computer graphics (images)

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.

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