On the number of perfect matchings in random polygonal chains

Autor: Wei Shouliu, Feng Yongde, Ke Xiaoling, Huang Jianwu
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Open Mathematics, Vol 21, Iss 1, Pp 755-759 (2023)
Druh dokumentu: article
ISSN: 2391-5455
DOI: 10.1515/math-2023-0146
Popis: Let GG be a graph. A perfect matching of GG is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics. But the enumeration problem of perfect matchings for general graphs (even in bipartite graphs) is non-deterministic polynomial (NP)-hard. Xiao et al. [C. Xiao, H. Chen, L. Liu, Perfect matchings in random pentagonal chains, J. Math. Chem. 55 (2017), 1878–1886] have studied the problem of perfect matchings for random odd-polygonal chain (i.e., with odd polygons). In this article, we further present simple counting formulae for the expected value of the number of perfect matchings in random even-polygonal chains (i.e., with even polygons). Based on these formulae, we obtain the average values of the number for perfect matchings with respect to the set of all even-polygonal chains with nn polygons.
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