2017/06/08 by Panpan Zhang, Zhang, Panpan · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1706.02441
openalex publication_date 2017/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, several properties of plain-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 variance of the degree variable via a \Polya urn approach. In addition, we look into a topological index, the Zagreb index, of this class of trees. We calculate the exact first two moments of the Zagreb index by using recurrence methods. We also provide several evidence in favor of our conjecture that the Zagreb index of PORTs do not follow a Gaussian law asymptotically. Lastly, we determine the limiting degree distribution in Poissonized PORTs, and show that it is exponential after being properly scaled.