Abstract
We determine conditions for the parameters n and δ, for which the general Randic 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 Randic index of trees and chemical trees are obtained.
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