On stress sum eigenvalues and stress sum energy of graphs

In this article, we introduce the stress sum matrix $SSM(G)$ for a graph $G$, which is related to the stress sum index. We explore the properties of this matrix, establish bounds on its eigenvalues, and define the stress sum energy $\mathcal{E}_{SS}(G)$ as the sum of the absolute eigenvalues. Additionally, we discuss its potential chemical relevance by comparing $\mathcal{E}_{SS}(G)$ with the $\pi$-electron energy of polyaromatic hydrocarbons.