A complete characterization for \(k\)-resonant Klein-bottle polyhexes

DOI10.1007/s10910-006-9178-6zbMath1148.05031OpenAlexW2063528026MaRDI QIDQ926910

Wai Chee Shiu, Heping Zhang

Publication date: 21 May 2008

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

Full work available at URL: https://doi.org/10.1007/s10910-006-9178-6

zbMATH Keywords

fullereneKekulé structureKlein bottle polyhex\(k\)-resonancetoroidal polyhex

Mathematics Subject Classification ID

Applications of graph theory (05C90) Planar graphs; geometric and topological aspects of graph theory (05C10) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (14)

Labelings of type \((1, 1, 1)\) for Klein bottle fullerenes ⋮ 2-resonance of plane bipartite graphs and its applications to boron-nitrogen fullerenes ⋮ Maximal resonance of cubic bipartite polyhedral graphs ⋮ On maximal resonance of polyomino graphs ⋮ Hexagonal resonance of (3,6)-fullerenes ⋮ Hexagonal systems with the one-to-one correspondence between geometric and algebraic Kekulé structures ⋮ On the restricted matching extension of graphs on the torus and the Klein bottle ⋮ On \(k\)-resonance of grid graphs on the plane, torus and cylinder ⋮ \(k\)-resonant toroidal polyhexes ⋮ 2-extendability and \(k\)-resonance of non-bipartite Klein-bottle polyhexes ⋮ Maximally resonant polygonal systems ⋮ Maximum cardinality resonant sets and maximal alternating sets of hexagonal systems ⋮ A mathematical programming model for computing the fries number of a fullerene ⋮ 2-extendability of toroidal polyhexes and Klein-bottle polyhexes

Cites Work

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• When each hexagon of a hexagonal system covers it
• \(k\)-resonance of open-ended carbon nanotubes
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• Uniqueness and faithfulness of embedding of toroidal graphs
• Resonance in elemental benzenoids
• The Clar covering polynomial of hexagonal systems. I
• \(k\)-resonance in toroidal polyhexes
• Construction and enumeration of regular maps on the torus
• Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface

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