Investigating several fundamental properties of random lobster trees and random spider trees
Published in Methodology and Computing in Applied Probability, 2021
Recommended citation: Ren, Y., Zhang, P. and Dey, D. K. (2022). " Investigating several fundamental properties of random lobster trees and random spider trees." Methodology and Computing in Applied Probability, 24(1), 431--447. https://doi.org/10.1007/s11009-021-09863-9
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.’