A note on the number of matchings and independent sets in trees

DOI10.1016/J.DAM.2004.07.001zbMath1056.05035OpenAlexW2017416969MaRDI QIDQ1765528

Miranca Fischermann, Lutz Volkmann, Dieter Rautenbach

Publication date: 23 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.dam.2004.07.001

zbMATH Keywords

MatchingStable setHosoya indexMerrifield-Simmons indexIndependent setTree

Mathematics Subject Classification ID

Trees (05C05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (8)

The largest Hosoya index of \((n,n+1)\)-graphs ⋮ The smallest Merrifield-Simmons index of \((n,n+1)\)-graphs ⋮ On the number of matchings of graphs formed by a graph operation ⋮ On the number of \(k\)-matchings in graphs ⋮ Closed formulas for the numbers of small independent sets and matchings and an extremal problem for trees ⋮ The smallest hosoya index in \((n,n+1)\)-graphs ⋮ The Merrifield-Simmons index and Hosoya index of \(C(n, k, \lambda)\) graphs ⋮ The minimum Merrifield-Simmons index of unicyclic graphs with diameter at most four

Cites Work

• On some counting polynomials in chemistry
• An introduction to matching polynomials
• Higher-order Fibonacci numbers
• On the theory of the matching polynomial
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