Sharp lower and upper bounds are established for the ratio σ₁(G)/σ₀(G) over connected graphs, trees, and forests.
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Ratio of the number of $\mathbf{1}$-nearly independent vertex subsets and the Merrifield-Simmons index
Sharp lower and upper bounds are established for the ratio σ₁(G)/σ₀(G) over connected graphs, trees, and forests.