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Investigating Several Fundamental Properties of Random Lobster Trees and Random Spider Trees

Author

Listed:
  • Yuxin Ren

    (Rochester Institute of Technology)

  • Panpan Zhang

    (University of Pennsylvania)

  • Dipak K. Dey

    (University of Connecticut)

Abstract

In this paper, we investigate several random structures, namely two classes of random lobster trees (RLTs) and a class of random spider trees (RSTs). The first class of RLTs grow with a fixed probability, whereas those from the second class evolve in a dynamic manner underlying a flavor of semi-opposite reinforcement. For these two classes, we characterize the structure of the random graphs therein via some probabilistic methods. In addition, we look into a class of RSTs that evolve in a preferential attachment manner. We characterize the structure of RSTs by determining the exact and asymptotic distributions of the number of leaves, and by computing two kinds of topological indices.

Suggested Citation

  • Yuxin Ren & Panpan Zhang & Dipak K. Dey, 2022. "Investigating Several Fundamental Properties of Random Lobster Trees and Random Spider Trees," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 431-447, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09863-9
    DOI: 10.1007/s11009-021-09863-9
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    References listed on IDEAS

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    1. Gao, Shuyang & Mahmoud, Hosam M., 2018. "A self-equilibrium Friedman-like urn via stochastic approximation," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 77-83.
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