On the Multiplicative Zagreb Indices of Bucket Recursive‎ ‎Trees

Document Type: Research Paper

Author

Imam Khomeini international university

Abstract

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consider the ratio of the multiplicative Zagreb‎ ‎indices for different values of $n$ and $b$‎. ‎All our results reduce to the ordinary recursive trees for $b=1$‎.

Keywords

Main Subjects


1. P. Billingsley, Probability and Measure, John Wiley and Sons, New York, 1995.
2. M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index,
MATCH Commun. Math. Comput. Chem. 68 (2012), 217–230.
3. A. Iranmanesh, M. A. Hosseinzadeh, I. Gutman, On multiplicative Zagreb indices
of graphs, Iranian J. Math. Chem. 3 (2012), 145–154.
4. R. Kazemi, Probabilistic analysis of the first Zagreb index, Trans. Comb. 2 (2013),
35–40.
5. R. Kazemi, Depth in bucket recursive trees with variable capacities of buckets, Acta
Math. Sin. Engl. Ser. 30 (2014), 305–310.
6. R. Kazemi, The eccentric connectivity index of bucket recursive trees, Iranian J.
Math. Chem. 5 (2014), 77–83.
7. H. M. Mahmoud, R. T. Smythe, Probabilistic analysis of bucket recursive trees,
Theoret. Comput. Sci. 144 (1995), 221–249.
8. A. Meir, J. W. Moon, On the altitude of nodes in random trees, Canadian J. Math.
30 (1978), 997–1015.
9. R. Todeschini, D. Ballabio, V. Consonni, Novel molecular descriptors based on
functions of new vertex degrees, in: I. Gutman, B. Furtula (Eds.), Novel Molecular
Structure Descriptors Theory and Applications I, Univ. Kragujevac, Kragujevac
(2010), 73–100.
10. R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors
based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem.
64 (2010), 359–372.