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On the Zagreb Index of Random Recursive Trees
- Source :
- J. Appl. Probab. 48, no. 4 (2011), 1189-1196
- Publication Year :
- 2011
- Publisher :
- Cambridge University Press (CUP), 2011.
-
Abstract
- We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.
- Subjects :
- Statistics and Probability
Random graph
Discrete mathematics
Stochastic process
General Mathematics
010102 general mathematics
Loop-erased random walk
Random tree
Zagreb index
Martingale central limit theorem
recursive tree
01 natural sciences
Random binary tree
Recursive tree
Combinatorics
05C05
010104 statistics & probability
martingale central limit theorem
60F05
60C05
0101 mathematics
Statistics, Probability and Uncertainty
Martingale (probability theory)
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 48
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....7790f242e04ae4848abd6375ea2b1a12