Abstract
Fullerene graphs are cubic, 3-connected, planar graphs with exactly 12 pentagonal faces, while all other faces are hexagons. Fullerene graphs are mathematical models of fullerene molecules, i.e., molecules comprised only by carbon atoms different than graphites and diamonds. We give a survey on fullerene graphs from our perspective, which could be also considered as an introduction to this topic. Different types of fullerene graphs are considered, their symmetries, and construction methods. We give an overview of some graph invariants that can possibly correlate with the fullerene molecule stability, such as: the bipartite edge frustration, the independence number, the saturation number, the number of perfect matchings, etc.
Highlights
The first fullerene molecule, with a structure like a football, was discovered experimentally in 1985 by Kroto et al [75]
We give a survey on fullerene graphs from our perspective, which could be considered as an introduction to this topic
We give an overview of some graph invariants that can possibly correlate with the fullerene molecule stability, such as: the bipartite edge frustration, the independence number, the saturation number, the number of perfect matchings, etc
Summary
The first fullerene molecule, with a structure like a football, was discovered experimentally in 1985 by Kroto et al [75]. Soon after the experimental discovery of the buckminsterfullerene, its existence in the nature was confirmed along with similar structures having 70, 76, 78, 82, 84, 90, 94, or 96 carbon atoms. Each of these all-carbon molecules have polyhedral structure, and all faces of the polyhedron are either pentagons or hexagons. All polyhedral molecules made entirely of carbon atoms are called fullerenes. The study from graph theoretical point of view has been motivated by a search for invariants that will correlate with their stability as a chemical compound. Later graph invariant were used in order to predict the physical and chemical properties of a fullerene compound. Special place among them have several interesting conjectures made by Graffiti, a conjecture making software [41]
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