An upper bound for the Clar number of fullerene graphs

DOI10.1007/s10910-006-9061-5zbMath1213.05259OpenAlexW2076423910MaRDI QIDQ1025749

Dong Ye, Heping Zhang

Publication date: 23 June 2009

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-006-9061-5

zbMATH Keywords

perfect matchingClar numberKekulé structurecarbon nanotubefullerene graphClar formulasextet pattern

Mathematics Subject Classification ID

Applications of graph theory (05C90) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (17)

A minimax result for perfect matchings of a polyomino graph ⋮ On the Clar number of graphene fragment ⋮ Nice pairs of disjoint pentagons in fullerene graphs ⋮ The fullerene graphs with a perfect star packing ⋮ A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of \(\text C_{60}\) ⋮ Sharp upper bounds on the Clar number of fullerene graphs ⋮ The complexity of the Clar number problem and an exact algorithm ⋮ Fullerenes with complete Clar structure ⋮ Leapfrog fullerenes have many perfect matchings ⋮ Extremal fullerene graphs with the maximum Clar number ⋮ Counting clar structures of \((4,6)\)-fullerenes ⋮ Hosoya entropy of fullerene graphs ⋮ Fullerenes with the maximum Clar number ⋮ Clar structures vs Fries structures in hexagonal systems ⋮ Clar structure and fries set of fullerenes and \((4,6)\)-fullerenes on surfaces ⋮ Packing resonant hexagons in fullerenes ⋮ 2-resonant fullerenes

Cites Work

• A comparison between 1-factor count and resonant pattern count in plane non-bipartite graphs
• Cyclical edge-connectivity of fullerene graphs and \((k,6)\)-cages
• \(k\)-resonance of open-ended carbon nanotubes
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