The expected subtree number index in random polyphenylene and spiro chains

The subtree number index STN(G) of a simple graph G is the number of nonempty subtrees of G. It is a structural and counting topological index that has received more and more attention in recent years. In this paper we first obtain exact formulas for the expected values of subtree number index of ra...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2020-10, Vol.285, p.483-492
Main Authors: Yang, Yu, Sun, Xiao-Jun, Cao, Jia-Yi, Wang, Hua, Zhang, Xiao-Dong
Format: Article
Language:English
Subjects:
Average value
Chains
Expected value
Expected values
Hexagons
Molecular chains
Polycyclic aromatic hydrocarbons
Random polyphenylene chain
Random spiro chain
Subtree number index
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Summary:The subtree number index STN(G) of a simple graph G is the number of nonempty subtrees of G. It is a structural and counting topological index that has received more and more attention in recent years. In this paper we first obtain exact formulas for the expected values of subtree number index of random polyphenylene and spiro chains, which are molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we establish a relation between the expected values of the subtree number indices of a random polyphenylene and its corresponding hexagonal squeeze. We also present the average values for subtree number indices with respect to the set of all polyphenylene and spiro chains with n hexagons.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.06.013