The Zagreb Index of Bucket Recursive Trees

Document Type: Original Scientific Paper


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

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



‎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.


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