The Number of Maximal Matchings in Polyphenylene Chains

Document Type : Research Paper

Authors

Department of Mathematics, Grand Valley State University, Allendale, MI, USA

Abstract

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also determine recurrences and generating functions for the sequences enumerating maximal matchings in several specific types of polyphenylenes and use these results to analyze the asymptotic behavior.

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References

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Iranian Journal of Mathematical Chemistry
Volume 10, Issue 4
December 2019
Pages 343-360

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