University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 10 4 2019 12 01 The Number of Maximal Matchings in Polyphenylene Chains 343 360 102515 10.22052/ijmc.2019.191800.1447 EN Taylor Short Department of Mathematics, Grand Valley State University, Allendale, MI, USA Zachary Ash Department of Mathematics, Grand Valley State University, Allendale, MI, USA Journal Article 2019 06 27 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. https://ijmc.kashanu.ac.ir/article_102515_9b04a5b392e022baa61e816c10095e99.pdf