Some properties of exponential trees

Exponential recursive trees and exponential PORTs are introduced in H. Mahmoud (Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021). In that reference, the author investigates the order and node profile of these species. Several other equa...

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Vydáno v:International journal of computer mathematics. Computer systems theory Ročník 7; číslo 1; s. 16 - 32
Hlavní autoři: Aguech, Rafik, Bose, Sudip, Mahmoud, Hosam, Zhang, Yi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis 02.01.2022
Témata:
degree profile
limit law
martingale
Network
Primary: 05082
random graph
Secondary: 60C05
ISSN:2379-9927, 2379-9935
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Shrnutí:Exponential recursive trees and exponential PORTs are introduced in H. Mahmoud (Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021). In that reference, the author investigates the order and node profile of these species. Several other equally important properties remain to be explored. The aim of the present manuscript is to establish fundamental properties concerning leaves (and their profile level by level) and distances in these trees. Some results fall back on the order of a tree. For the number of leaves in both flavours, we find (under appropriate scaling for each) a limit distribution uniquely characterized by inductively constructed moments. We find an limit for the scaled total (external) path length in an exponential recursive tree (PORT) in terms of the known distribution of the scaled order given in Mahmoud [11]. These total path lengths are indicative of the depth of a randomly chosen node (external node) in an exponential recursive tree (PORT).
ISSN:2379-9927
2379-9935
DOI:10.1080/23799927.2021.1974569