James Avery - Academia.edu (original) (raw)
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National Institute for Research and Development of Isotopic and Molecular Technologies
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Regular fullerenes are cubic planar connected graphs consisting of pentagons and hexagons only an... more Regular fullerenes are cubic planar connected graphs consisting of pentagons and hexagons only and come in many different shapes. There has been great progress over the last two decades describing the topological and graph theoretical properties of fullerenes, but leaving still many unsolved and interesting mathematical and chemical problems open in this field. For example, i) how to generate all possible fullerene isomers for a fixed atom count (where an efficient algorithm was introduced only very recently) ii) are fullerenes Hamiltonian (Barnette's conjecture) and what is the number of distinct Hamiltonian cycles (longest carbon chains), iii) the Pauling bond order and the number of different Kekulé structures (perfect matchings), iv) the search for suitable topological (chemical) indices to find the most stable fullerene structure out of the many (∼ N 9 ) possibilities, or how to pack fullerenes in 3D space (the Hilbert problem) to name but a few. Here we present a general overview on recent topological and graph theoretical developments in fullerene research over the past two decades.
Regular fullerenes are cubic planar connected graphs consisting of pentagons and hexagons only an... more Regular fullerenes are cubic planar connected graphs consisting of pentagons and hexagons only and come in many different shapes. There has been great progress over the last two decades describing the topological and graph theoretical properties of fullerenes, but leaving still many unsolved and interesting mathematical and chemical problems open in this field. For example, i) how to generate all possible fullerene isomers for a fixed atom count (where an efficient algorithm was introduced only very recently) ii) are fullerenes Hamiltonian (Barnette's conjecture) and what is the number of distinct Hamiltonian cycles (longest carbon chains), iii) the Pauling bond order and the number of different Kekulé structures (perfect matchings), iv) the search for suitable topological (chemical) indices to find the most stable fullerene structure out of the many (∼ N 9 ) possibilities, or how to pack fullerenes in 3D space (the Hilbert problem) to name but a few. Here we present a general overview on recent topological and graph theoretical developments in fullerene research over the past two decades.