The Expected Values of Hosoya Index and Merrifield-Simmons Index of Random Hexagonal Cacti

TL;DR

This paper derives generating functions and asymptotic behaviors for the expected Hosoya and Merrifield-Simmons indices of random hexagonal cacti, extending previous work and linking topological descriptors to physical properties of hydrocarbons.

Contribution

It establishes new generating functions and asymptotic formulas for the expected indices of random hexagonal cacti, generalizing prior results from 2010.

Findings

Derived generating functions for expected indices

Established asymptotic behaviors of the indices

Extended previous results to broader classes of cacti

Abstract

Hosoya index and Merrifield-Simmons index are two well-known topological descriptors that reflex some physical properties, boiling point or heat of formation for instance, of bezenoid hydrocarbon compounds. In this paper, we establish the generating functions of the expected values of these two indices of random hexagonal cacti. This generalizes the results of Doslic and Maloy, published in Discrete Mathemaics, in 2010. By applying the ideas on meromorphic functions and the growth of power series coefficients, the asymptotic behaviors of these indices on the random cacti have been established.