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

Yuxin Ren (), Panpan Zhang () and Dipak K. Dey ()
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Yuxin Ren: Rochester Institute of Technology
Panpan Zhang: University of Pennsylvania
Dipak K. Dey: University of Connecticut

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 431-447

Abstract: 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.

Keywords: Combinatorial probability; Degree profile; Lobster trees; Spider trees; Topological index; Primary: 05C05, 60C05; Secondary: 05C07, 62E20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09863-9

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