QSPR model for bond energy of Y-junction nanotubes through M, NM-polynomials based on reverse, reduced reverse degree and neighborhood degree based topological indices

Abstract

Abstract M polynomials and NM polynomials are integral concepts in polynomial graph theory. M polynomials, like the matching polynomial, provide insights into matching structures in graphs, while NM polynomials extend this to non-matching edges. These tools are crucial in understanding graph properties and are applied in diverse fields such as network design and chemistry. Often topological indices are derived from these polynomials, which are used in Quantitative Structure Activity Relations (QSAR)/ Quantitative Structure Property Relations (QSPR) studies that have applications in protein structure analysis, network communication optimization, drug design, drug discovery, pharmacokinetics, etc. In this paper, we have defined M, NM polynomials for reverse, reduced reverse, neighborhood reverse and neighborhood reduced reverse topological indices. And we have derived closed form expressions for topological indices from these polynomials for Y junction nanotubes. Also as an application we have developed a QSPR model for an important thermodynamic property, viz., bond energy, of Y-junction nanotubes using indices derived from the defined polynomials Mr, Mrr, NMr, NMrr. The QSPR model developed here is statistically robust with an R2 of 0.999, with marginal error and high F value, hence serves as a justification to our new definitions for more polynomials, topological indices to the ever increasing set.