Perfect Matchings in Random Octagonal Chain Graphs

Let G G be a graph. A perfect matching of G G 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 n n polygons.

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Perfect Matchings in Random Octagonal Chain Graphs

Cited by 2 publications

References 14 publications

The Counting of Perfect Matchings on Some Special Graphs

The Counting of Perfect Matchings on Some Special Graphs

On the number of perfect matchings in random polygonal chains

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