University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 The Zagreb Index of Bucket Recursive Trees 103 111 109509 10.22052/mir.2020.204312.1166 EN Ramin Kazemi Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran Ali Behtoei Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran Akram Kohansal Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran Journal Article 2019 10 07 ‎Bucket recursive trees are an interesting and natural generalization of recursive trees‎. ‎In this model the nodes are buckets that can hold up to b≥ 1 labels‎. ‎The (modified) Zagreb index of a graph is defined as the sum of‎ ‎the squares of the outdegrees of all vertices in the graph‎. ‎We give the mean and variance of this index in random bucket recursive trees‎. ‎Also‎, ‎two limiting results on this index are given‎. https://mir.kashanu.ac.ir/article_109509_f3b0cb23045fab361dda93a3b444fa84.pdf