The total number of matchings of a graph is defined as its Hosoya index. Conjugated and non-conjugated acyclic graphs that have maximal Hosoya index and short diameter are characterized in this paper, explicit expressions of the Hosoya indices of these extremal graphs are also presented.
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Ou, J. On acyclic molecular graphs with maximal Hosoya index, energy, and short diameter. J Math Chem 43, 328–337 (2008). https://doi.org/10.1007/s10910-006-9199-1
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DOI: https://doi.org/10.1007/s10910-006-9199-1