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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
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
- 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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