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ON SEVERAL PROPERTIES OF A CLASS OF PREFERENTIAL ATTACHMENT TREES—PLANE-ORIENTED RECURSIVE TREES

Published online by Cambridge University Press:  15 May 2020

Panpan Zhang Open the ORCID record for Panpan Zhang [Opens in a new window]
Panpan Zhang*
Affiliation:
Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA19104, USA E-mail: panpan.zhang@pennmedicine.upenn.edu
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Abstract

In this paper, several properties of a class of trees presenting preferential attachment phenomenon—plane-oriented recursive trees (PORTs) are uncovered. Specifically, we investigate the degree profile of a PORT by determining the exact probability mass function of the degree of a node with a fixed label. We compute the expectation and the variance of degree variable via a Pólya urn approach. In addition, we study a topological index, Zagreb index, of this class of trees. We calculate the exact first two moments of the Zagreb index (of PORTs) by using recurrence methods. Lastly, we determine the limiting degree distribution in PORTs that grow in continuous time, where the embedding is done in a Poissonization framework. We show that it is exponential after proper scaling.

Keywords

degree distributionplane-oriented recursive treesPoissonizationPólya urnpreferential attachmentZagreb index
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021 , pp. 839 - 857
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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