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Updated: Aug 5, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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An effective technique for developing the graphical polynomials of certain molecular graphs.

Ibtisam Masmali1, Muhammad Nadeem2, Awais Yousaf2

  • 1Department of Mathematics, College of Science, Jazan University, 45142, Jazan, Saudi Arabia.

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|March 24, 2023
PubMed
Summary
This summary is machine-generated.

Researchers developed a new method to create counting polynomials for complex chemical structures. This aids in understanding graph partitioning and the topology of fused Starphene and Kekulenes graphs.

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Area of Science:

  • * Mathematical chemistry
  • * Graph theory
  • * Chemical graph theory

Background:

  • * The Counting Polynomial, introduced by G. Polya in 1936, is a mathematical function with applications in chemistry.
  • * Its coefficients represent graph partitions and their frequencies, offering insights into molecular structures.
  • * Understanding these polynomials is crucial for analyzing complex chemical architectures.

Purpose of the Study:

  • * To develop a novel and efficient method for constructing counting polynomials.
  • * To apply this method to zigzag-edge coronoids formed by fusing Starphene and Kekulenes graphs.
  • * To expand knowledge in chemical graph theory and topological analysis.

Main Methods:

  • * Development of an efficient algorithm for generating counting polynomials.
  • * Application of the method to specific fused polycyclic aromatic hydrocarbons (PAHs).
  • * Analysis of graph partitioning within the coefficients of the constructed polynomials.

Main Results:

  • * Successful construction of counting polynomials for the specified zigzag-edge coronoids.
  • * Identification of partition frequencies through polynomial coefficients.
  • * Demonstration of the method's efficiency and applicability.

Conclusions:

  • * The developed method provides a valuable tool for analyzing complex chemical structures.
  • * Findings offer potential insights into the topology of fused Starphene and Kekulenes systems.
  • * This research contributes to the advancement of mathematical chemistry and graph theory applications.