On the Multiplicative Zagreb Indices of Bucket Recursive Trees

Abstract

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consider the ratio of the multiplicative Zagreb‎ ‎indices for different values of $n$ and $b$‎. ‎All our results reduce to the ordinary recursive trees for $b=1$‎.