Kepler stress exponential for graphs

In 1953, Alfonso Shimbel introduced the concept of vertex stress in a graph. The stress of a vertex in a graph is the number of shortest paths passing through it. This paper describes the Kepler stress exponential $KS(G,x)$ of graphs and presents findings, including a characterization of graphs with non-zero constant vertex stress polynomials. Similarly, we established the importance of the Kepler stress exponential in predicting the physicochemical properties of butane derivatives.