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On Several Properties of A Class of Hybrid Recursive Trees

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  • Panpan Zhang

    (Vanderbilt University Medical Center
    Vanderbilt University Medical Center)

Abstract

In this paper, we propose a class of random trees, the evolution of which is an integration of uniform and preferential attachments. Hence, they are called hybrid recursive trees (HRTs). The goal of this paper is to characterize the structure of HRTs. At first, we investigate the degree profile of HRTs by determining the exact and asymptotic mean of the degree of a node with fixed label. Next, we show that the limit distribution of the number of leaves of HRTs is Gaussian, and that the degree distribution follows a power law, suggesting that HRTs are scale-free. At last, we look into the Zagreb index of HRTs, where the first two moments are calculated.

Suggested Citation

  • Panpan Zhang, 2023. "On Several Properties of A Class of Hybrid Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-20, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09988-z
    DOI: 10.1007/s11009-023-09988-z
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    References listed on IDEAS

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    1. Hosam M. Mahmoud, 2014. "The Degree Profile in Some Classes of Random Graphs that Generalize Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 527-538, September.
    2. Tiandong Wang & Panpan Zhang, 2022. "Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 957-986, October.
    3. Panpan Zhang & Xiaojing Wang, 2022. "Several Topological Indices of Random Caterpillars," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1773-1789, September.
    Full references (including those not matched with items on IDEAS)

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    1. Panpan Zhang & Hosam M. Mahmoud, 2020. "On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 625-645, June.

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