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Independent set-based multivariate graph polynomials for fractal-type silicate triangle structures
K S Nithiya1, D Easwaramoorthy1
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
Frontiers in Chemistry
|July 28, 2026
Summary
This study introduces a novel computational method to analyze fractal silicate triangle graphs using independence polynomials. The research provides insights into the combinatorial and structural properties of these complex self-similar mineral structures.
Area of Science:
- Mineralogy and Materials Science
- Graph Theory and Combinatorics
- Computational Chemistry
Background:
- Silicate structures are mineral materials known for their complexity and self-similarity.
- Fractal theory and graph polynomials are effective tools for analyzing intricate structures.
- Independence polynomials represent molecular graphs and analyze adjacency relationships.
Purpose of the Study:
- To explore fractal-type silicate triangle graphs as a class of self-similar graphs.
- To develop a computational approach for evaluating independence polynomials of these graphs.
- To analyze the combinatorial and structural characteristics of fractal silicate graphs.
Main Methods:
- Utilizing graph theory and fractal analysis.
- Developing a computational algorithm for evaluating independence polynomials.
- Employing SAGE mathematical software for computations and graphical analysis.
Main Results:
- An innovative computational approach was presented for evaluating independence and multivariate independence polynomials.
- The algorithm systematically identifies independent sets and computes associated polynomials.
- Graphical analysis provided insights into the structural properties of fractal silicate triangle graphs at specific iterations (n=1, 2, 3).
Conclusions:
- The study successfully demonstrated a computational method for analyzing fractal silicate triangle graphs.
- The findings offer deeper insights into the self-similar and combinatorial properties of these mineral structures.
- This approach can be extended to analyze other complex graph structures in materials science and chemistry.
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