The Clar covering polynomial of hexagonal systems. I

DOI10.1016/0166-218X(95)00081-2zbMath0859.05070OpenAlexW2014331704MaRDI QIDQ1923607

Heping Zhang, Fu Ji Zhang

Publication date: 7 April 1997

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.elsevier.com/locate/dam

zbMATH Keywords

hexagonal systemKekulé structuresClar covering polynomialHerndon number

Mathematics Subject Classification ID

Applications of graph theory (05C90) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (30)

Analytic properties of sextet polynomials of hexagonal systems ⋮ ZZ Polynomials of Regular m-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 3. Compilation of Results for m=1-6 ⋮ Zhang-Zhang polynomials of cyclo-polyphenacenes ⋮ Algorithm for generating generalized resonance structures of single zigzag chains based on interface theory ⋮ The Clar covering polynomial of hexagonal systems with an application to chromatic polynomials ⋮ Hypergraphs and the Clar problem in hexagonal systems ⋮ The number of \(n\)-cycles in a graph ⋮ Unnamed Item ⋮ Some algebraic polynomials and topological indices of generalized prism and toroidal polyhex networks ⋮ Some computational aspects of boron triangular nanotubes ⋮ Some invariants of Jahangir graphs ⋮ Sharp upper bounds on the Clar number of fullerene graphs ⋮ Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: prolate rectangles and their generalizations ⋮ Topological indices and graph entropies for carbon nanotube Y-junctions ⋮ Resonance graphs on perfect matchings of graphs on surfaces ⋮ Some invariants of flower graph ⋮ Unnamed Item ⋮ A complete characterization for \(k\)-resonant Klein-bottle polyhexes ⋮ \(k\)-resonant toroidal polyhexes ⋮ Unnamed Item ⋮ Relations between Clar structures, Clar covers, and the sextet-rotation tree of a hexagonal system ⋮ Equivalence between Clar covering polynomials of single zigzag chains and tiling polynomials of \(2 \times n\) rectangles ⋮ Counting clar structures of \((4,6)\)-fullerenes ⋮ Unnamed Item ⋮ \(k\)-resonance in toroidal polyhexes ⋮ Fullerenes with the maximum Clar number ⋮ Enumeration of Clar covers of parallelogram chains ⋮ Complete forcing numbers of hexagonal systems ⋮ M-polynomials and topological indices of linear chains of benzene, napthalene and anthracene ⋮ The generalized Zhang-Zhang polynomial of benzenoid systems -- theory and applications

Cites Work

• A maximal cover of hexagonal systems
• On some counting polynomials in chemistry
• Alternating 6-cycles in perfect matchings of graphs representing condensed benzenoid hydrocarbons
• On a general class of graph polynomials
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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