The Clar covering polynomial of hexagonal systems with an application to chromatic polynomials

DOI10.1016/S0012-365X(96)00279-8zbMath0884.05085MaRDI QIDQ1366789

Heping Zhang

Publication date: 17 September 1997

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

zbMATH Keywords

perfect matchingchromatic polynomialsClar numberhexagonal systemClar covering polynomialClar cover

Mathematics Subject Classification ID

Applications of graph theory (05C90) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Coloring of graphs and hypergraphs (05C15) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (9)

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 number of \(n\)-cycles in a graph ⋮ Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures: prolate rectangles and their generalizations ⋮ Equivalence between Clar covering polynomials of single zigzag chains and tiling polynomials of \(2 \times n\) rectangles ⋮ Counting clar structures of \((4,6)\)-fullerenes ⋮ Kekulé structures of hexagonal chains -- some unusual connections ⋮ Enumeration of Clar covers of parallelogram chains

Cites Work

• On some counting polynomials in chemistry
• When each hexagon of a hexagonal system covers it
• Connections between the matching and chromatic polynomials
• An introduction to matching polynomials
• The Clar covering polynomial of hexagonal systems. I
• The Clar covering polynomial of hexagonal systems. III
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