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2019.
A note on maximal matchings in rooted products of paths and short cycles
A matching M in a graph G is maximal if it cannot be extended to a larger matching in G. The enumerative properties of maximal matchings are much less known and researched than for maximum and perfect matchings. In this paper we present the recurrences and generating functions for the sequences enumerating maximal matchings in rooted products of paths and short cycles. We also analyze the asymptotic behavior of those sequences.