This analysis calculates moments of the zagreb index in recursive trees, suggesting convergence for the root degree.
The Zagreb index of a graph is the sum of the squared degrees of all nodes in the graph. In this note, we study the Zagreb index of exponential plane-oriented recursive trees. We first show the convergence in L 2 for the root degree. Then we calculate the first two moments of the Zagreb index from a recurrence. Finally, the limit law for the Zagreb index of an exponential plane-oriented recursive tree is characterized by an application of the contraction method.
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Fathi et al. (2025) studied this question.
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