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The number of maximal matchings in polygon rings

2025/06/10 by Chengqi Li, Li, Chengqi, Jinhui Yin +3
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2506.08687

openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A matching of graph G is maximal if it cannot be expanded by adding any edge to create a larger matching. In this paper, for a hexagonal ring H with n hexagons, we show that the number of maximal matchings of H equals to the trace of the product of n matrices, each of which is S, L, or R according to the type of the connection mode of H. Finally, we extend this conclusion to arbitrary polygon rings and provide an algorithm to determine the transition matrices of polygon chains (rings).

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