The Hosoya index is equal to total number of matchings and the Merrifield-Simmons index is equal to total number of independent sets. The Hosoya index of cyclic alkanes, the Hosoya index and the Merrifield-Simmons index of 1-methyl bicyclo [X.1.0] alkanes are possess same value which is represented by Lucas sequence. In this paper we investigate these molecular graphs in terms of matchings and independent sets.
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