The Zagreb Index of Bucket Recursive Trees

نویسندگان
Kazemi, Ramin ID 1
Kohansal, Akram ID 2
Behtoei, Ali ID 3

1 Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran

2 Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran

3 Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran

doi
10.22052/mir.2020.204312.1166
چکیده

‎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.

کلیدواژه‌ها
Bucket recursive tree‎, ‎the Zagreb index‎, Limiting rule‎