Abstract
A perfect matching of a (molecule) graph G is a set of independent edges covering all vertices in G . In this paper, we establish a simple formula for the expected value of the number of perfect matchings in random octagonal chain graphs and present the asymptotic behavior of the expectation.
Highlights
A general problem of interest in chemistry, physics, and mathematics is the enumeration of perfect matchings, on lattices and graphs
A perfect matching of G is a set of independent edges covering all vertices in G, which is called Kekulestructure in organic chemistry and closed-packed dimer in statistical physics
There are strong connections between the number of the Kekulestructures and chemical properties for many molecules such as benzenoid hydrocarbons [1,2,3]. e number of Kekulestructures is an important topological index which had been applied for estimation of the resonant energy and total π-electron energy [2, 4] and Clar aromatic sextet [5]
Summary
A general problem of interest in chemistry, physics, and mathematics is the enumeration of perfect matchings, on lattices and (molecule) graphs. Denote the number of perfect matchings of a graph G by Φ(G). Yang and Zhao [12] presented a relation between the number of perfect matching in octagonal chain graphs and Hosoya index of the caterpillar trees in 2013. Wei et al [13]discussed the Wiener indices in a type of random octagonal chains in 2018.
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