Stress Sum Energy of Graphs

The stress sum matrix SSM(G)=(s_ij ) of a graph G whose vertex v_i has stress centrality st(v_i), is defined as s_ij=st(v_i) + st(v_j ), if the vertices v_i and v_j are adjacent, otherwise s_ij=0. The eigenvalues of SSM(G) are known as stress sum eigenvalues and the stress sum energy is the sum of the absolute values of the stress sum eigenvalues. The spectral properties of the stress sum matrix of some classes of graphs are explored in this article. The main contribution of the article is that the stress sum energy of a graph, obtained by means of various graph products like the subdivision graph and shadow graph, is investigated, and well-established relations are derived in terms of their base graphs.