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

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-oppo...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 24; no. 1; pp. 431 - 447
Main Authors Ren, Yuxin, Zhang, Panpan, Dey, Dipak K.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2022
Springer Nature B.V
Subjects
Business and Management
Chemistry
Combinatorics
Economics
Electrical Engineering
Graphs
Life Sciences
Mathematics and Statistics
Probabilistic methods
Random variables
Statistical analysis
Statistics
Trees (mathematics)
Topological index
62E20
Combinatorial probability
Primary: 05C05
Lobster trees
Spider trees
Degree profile
60C05; Secondary: 05C07
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Summary: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.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-021-09863-9