What question did this study set out to answer?

The aim is to analyze the Zagreb index in exponential plane-oriented recursive trees and understand its statistical properties.

February 5, 20260 citations

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Zagreb index in exponential plane-oriented recursive trees

RFRonak Fathi MJMehri Javanian

Key Points

The aim is to analyze the Zagreb index in exponential plane-oriented recursive trees and understand its statistical properties.
Studied the convergence in L2 for the root degree.
Calculated the first two moments of the Zagreb index using a recurrence relation.
Characterized the limit law for the Zagreb index through the contraction method.
Demonstrated convergence in L2 for the root degree of the trees.
Derived explicit expressions for the first two moments of the Zagreb index.
Characterized the limit distribution of the Zagreb index indicating its statistical behavior.

Abstract

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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Cite This Study

Fathi et al. (Tue,) studied this question.

synapsesocial.com/papers/6984347ff1d9ada3c1fb2b24 https://doi.org/https://doi.org/10.1051/ita/2025003/pdf

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