On the Zagreb index of random recursive trees

Abstract

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Z_n, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Z_n - E[Z_n], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.