This note explores the Zagreb index characteristics of exponential plane-oriented recursive trees, indicating significant findings on convergence and moments.
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 L2 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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