On the Zagreb index of random m-oriented recursive trees

Abstract

The main goal of this paper is to study the modified $F$-indices (modified first Zagreb index and modified forgotten topological index) of random $m$-oriented recursive trees (RMORTs). First, through two recurrence equations, we compute the mean and the variance of these indices in our random tree model. Second, we show four convergence in probability based on these indices. Third, the asymptotic normalities, through the martingale central limit theorem, are given.

Keywords

• random m-oriented recursive tree‎
• modified ‎ f-indices‎ ‎
• ‎ limiting rule&lrm