University of KashanMathematics Interdisciplinary Research2538-36395220201201The Zagreb Index of Bucket Recursive Trees10311110950910.22052/mir.2020.204312.1166ENRaminKazemiDepartment of Statistics, Imam Khomeini International University, Qazvin, I. R. IranAliBehtoeiDepartment of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. IranAkramKohansalDepartment of Statistics, Imam Khomeini International University, Qazvin, I. R. Iranhttps://orcid.org/0000-0002-1894-411XJournal Article20191007Bucket 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.http://mir.kashanu.ac.ir/article_109509_f3b0cb23045fab361dda93a3b444fa84.pdf