The Sanskruti index of trees and unicyclic graphs

The Sanskruti index of a graph G is defined as S(G)=∑uv∈E(G)sG(u)sG(v)sG(u)+sG(v)−23,$$\begin{align*}S(G)=\sum_{uv\in{}E(G)}{\left(\frac{s_G(u)s_G(v)}{s_G(u)+s_G(v)-2}\right)}^3, \end{align*}$$where sG(u) is the sum of the degrees of the neighbors of a vertex u in G. Let Pn, Cn, Sn and Sn + e be the path, cycle, star and star plus an edge of n vertices, respectively. The Sanskruti index of a molecular graph of a compounds can model the bioactivity of compounds, has a strong correlation with entropy of octane isomers and its prediction power is higher than many existing topological descriptors.