A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. In this paper, we determine the lower bound for the Hosoya index in (n, n + 1)-graphs in terms of the order n, and characterize the (n, n + 1)-graph with the smallest Hosoya index.
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Deng, H. The smallest Hosoya index in (n, n + 1)-graphs. J Math Chem 43, 119–133 (2008). https://doi.org/10.1007/s10910-006-9186-6
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DOI: https://doi.org/10.1007/s10910-006-9186-6