We determine conditions for the parameters n and δ, for which the general Randić index R δ is not an acceptable index of branching of n-vertex trees, i.e., for which the n-vertex star and the n-vertex path have not extremal R δ-values among all n-vertex trees. Analogous results are established also in the case of n-vertex chemical trees. Numerous other results for the general Randić index of trees and chemical trees are obtained.
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Clark, L., Gutman, I. The exponent in the general Randić index. J Math Chem 43, 32–44 (2008). https://doi.org/10.1007/s10910-006-9177-7
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DOI: https://doi.org/10.1007/s10910-006-9177-7