On the Sanskruti index of graphs

The topological indices are important tools in the chemical graph theory to model different physico-chemical properties of molecules. The Sanskruti index for a graph G having vertex set V(G) and edges set E(G) is defined as S(G)=∑uv∈E(G)(δG(u)δG(v)δG(u)+δG(v)-2)3,where δ_G(u) represents the degree sum of nodes adjacent to u∈ V(G). In this report, we argue that the chemical applicability of the S-index in the paper (Hosamani in J Appl Math Comput 54:425–433, 2017) is investigated incorrectly. In addition to correcting the result, we perform a comprehensive investigation to uncover the chemical significance of S. Some interesting mathematical features of the index are also explored by deriving some tight bounds with identifying the extremal graphs.