Total tension as a topological index

In this article, we see the total tension of a graph as a topological index and establish a relation between total tension index and total stress of a graph. We deduce that a graph is complete if and only if its total tension and the number of geodesics in it are equal. We also deduce that the total tension of an n-vertex connected proper subgraph of a complete graph Kn with n >= 3 vertices is greater than the total tension of Kn. We obtain a formula for computing total tension of a tree. Further, a QSPR analysis has been carried to demonstrate that total tension index can be used as a predictive measure for physical properties of lower alkanes. Linear regression models involving total tension index have been presented for some physical properties of lower alkanes.