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Because of the numerous applications to mathematical chemistry and statistical physics, the number of matchings of a molecular graph has been studied extensively not only by mathematicians but also by physicists and chemists. In this paper, we consider the problem on enumeration of matchings of the silicate molecular graphs and derive the exact formula of the number of matchings of two classes of silicate molecular graphs. Particularly, we show that these two classes of silicate molecular graphs have the same matching entropy.

On the Number of Matchings of Two Classes of Silicate Molecular Graphs