The expected subtree number index in random polyphenylene and spiro chains

TL;DR

This paper derives exact formulas for the expected subtree number index in random polyphenylene and spiro chains, providing insights into their structural properties and relationships with related molecular graphs.

Contribution

It introduces new exact formulas for expected subtree number indices in specific molecular graph classes and explores their relationships with hexagonal squeeze graphs.

Findings

Exact formulas for expected subtree number indices in random polyphenylene and spiro chains.

A relation between subtree indices of a chain and its hexagonal squeeze.

Average subtree number indices for all chains with n hexagons.

Abstract

Subtree number index $\emph{STN}(G)$ of a graph $G$ is the number of nonempty subtrees of $G$. It is a structural and counting based 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.