Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates

Abstract

Quantitative structure-activity relationship (QSAR) represents quantitative correlation of chemical structural features called as molecular descriptors and pharmacological activity as response endpoints. Topological index is a molecular descriptor extensively used to study QSAR of pharmaceuticals to assess their molecular characteristics by numerical computation. Theoretical assessment of drug like molecules helps to expedite the drug design and discovery process by rationalizing the lead identification, lead optimization and understanding their mechanism of actions. Therefore, in this article, we have computed the general inverse sum indeg index, ${\mathrm{ISI}}_{\left(\alpha ,\beta \right)}$ of Hyaluronic acid-curcumin conjugates by using molecular structure analysis and edge partitioning technique. Many standard topological indices are obtained as a special case of ${\mathrm{ISI}}_{\left(\alpha ,\beta \right)}$ . We also proposed general inverse sum indeg polynomial ${\mathrm{ISI}}_{\left(\alpha ,\beta \right)}(G_n,x)$ of Hyaluronic acid-curcumin conjugates from which many well-known polynomials are deduced.

Keywords: Curcumin; Degree-based topological indices; Hyaluronic acid; Hyaluronic acid-curcumin conjugates; Polynomials.

Fig. 1

An illustration representing motivation of the current study.

Fig. 2

The molecular structure of hyaluronic acid-curcumin conjugates.

Fig. 3

Corresponding molecular graph of hyaluronic acid-curcumin conjugates $G_1:n=1$.

Fig. 4

Corresponding molecular graph of hyaluronic acid-curcumin conjugates $G_2:n=2$.

Fig. 5

Corresponding molecular graph of hyaluronic acid-curcumin conjugates $G_3:n=3$.