The general Randić index of trees with given number of pendent vertices

The general Randic index of a graph G is defined as R α ( G ) = ź u v ź E ( G ) ( d ( u ) d ( v ) ) α , where d(u) denotes the degree of a vertex u in G and α is a real number. In this paper, we determine the maximum general Randic indices of trees and chemical trees with n vertices and k pendent vertices for 4 ź k ź ź n + 2 3 ź and α0 ź α < 0, where α 0 ź - 0.5122 is the unique non-zero root of the equation 6 ź 4 α - 20 ź 9 α + 10 ź 12 α - 16 α + 5 ź 24 α = 0 . The corresponding extremal graphs are also characterized.

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