M, NM-polynomials Based on Reverse, Reduced Reverse Degree and Neighborhood Degree Based Topological Indices with Applications to Bond Energy of Y-Junction Nanotubes.

Abstract

Background: In graph theory, M polynomials like the matching polynomial are very crucial in examining the matching structures within graphs, while NM polynomials extends this to analyze non-matching edges. These polynomials are important in many fields, including chemistry and network architecture. They support the derivation of topological indices for protein structure analysis, network communication optimization, and drug design in QSAR/QSPR investigations.

Objective: The aim of this paper is to define novel M and NM polynomials for different topological indices and to derive their closed-form expressions, specifically for Y-junction nanotubes. These new polynomials and indices are employed to create a robust QSPR model to predict bond energy in Y-junction nanotubes, that provide high accuracy and reliability in the model's statistical performance.

Method: This paper introduces new forms of M and NM polynomials tailored to specific topological indices related to reverse and neighborhood reverse properties. We derive closed-form expressions for these indices in Y-junction nanotubes. Furthermore, we develop a QSPR model to predict bond energy in Y-junction nanotubes using the newly defined indices.

Result: We define novel M and NM polynomials for various topological indices and derive precise expressions for Y-junction nanotubes. Utilizing these indices, we construct a highly accurate QSPR model (R² = 0.999) for predicting bond energy in Y-junction nanotubes, confirming the validity of our polynomial definitions and indices.

Conclusion: We have presented new M and NM polynomials for different topological indices and derive their expressions specifically for Y-junction nanotubes. With these newly defined indices, we have developed a highly precise QSPR model to predict bond energy, achieving an R² value of 0.999. This work underscores the effectiveness of our polynomial definitions and indices in predicting material properties.