Acta Mechanica Slovaca 2025, 29(4):6-21 | DOI: 10.21496/ams.2026.003

Mathematical Modeling to Compute Topological Indices of Some Polymers Using Graph Polynomials

Muhammad Irfan1, *, Amina Rasool1, Khalid Pervaiz2, Hamood Ur Rehman1
1 Department of Mathematics, University of Okara, Okara, Pakistan
2 Department of Chemistry, University of Okara, Okara, Pakistan

Graph theory offers powerful tools for modeling, designing, analyzing, and understanding the features of chemical structures and networks. In this framework, atoms are represented as vertices and chemical bonds as edges, forming a molecular graph. This paper focuses on the chemical graphs of Styrene Acrylonitrile (SAN) and Acrylonitrile Butadiene Styrene (ABS). Styrene Acrylonitrile (SAN) copolymers have been available since 1940. Their increased toughness compared to styrene made them suitable for various applications. However, SAN's limitations led to the addition of rubber (butadiene) as a third monomer, giving rise to Acrylonitrile Butadiene Styrene (ABS) plastics. ABS copolymers were introduced in the 1950's and became popular due to their variability and ease of processing, establishing them as the most widely used engineering polymers. In this study, we compute several topological indices of the SAN and ABS chemical graphs using M-Polynomial and NM-Polynomial Methods. Specifically, we calculate the First Zagreb index, Second Zagreb index, Modified Second Zagreb index, Third Redefine Zagreb index, Symmetric Division index , General Randi´c index, Forgotten index, Inverse index, and Harmonic index. These indices are widely used in various fields, such as drug discovery, molecular modeling, and other molecular research areas. These indices enable the establishment of connections between specific physicochemical properties of chemical compounds, such as stability, boiling point, entropy, strain energy, and heat of formation.

Received: February 1, 2026; Revised: February 13, 2026; Accepted: February 13, 2026; Published: December 15, 2025  Show citation

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Irfan, M., Rasool, A., Pervaiz, K., & Rehman, H.U. (2025). Mathematical Modeling to Compute Topological Indices of Some Polymers Using Graph Polynomials. Acta Mechanica Slovaca, 29(4), 6-21. doi: 10.21496/ams.2026.003
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