The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees

The zeroth-order Randic index and sum-connectivity index are two indices based on the vertex degrees. They appeared in the topological formula for the total π-electron energy of conjugated molecules and attracted a lot of attention in recent years. Let T n be the set of trees of order n. Suppose each tree in T n is equally likely. We get that for almost every tree, the zeroth-order Randic index is among (r1 ? e)n and the sum-connectivity index is among (r2 ? e)n, where r1, r2 are some constants and e is any positive real number.

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