Neighbors stress sum energy of graphs

Abstract

In this article, we introduced the concept of the Neighbors Stress Sum of a vertex and a new matrix for a connected graph G. In this matrix, the sum of the i-th row and the i-th column are both equal to the Neighbors Stress Sum of the i-th vertex. Additionally, we define a new graph energy variant called the Neighbors Stress Sum Energy, denoted as E<inf>NSS</inf>(G), for a graph G. Further, we established bounds, and characterized the largest eigenvalue of NSS(G).