Degree Square Sum Energy of Graphs

Abstract

Degree square sum matrix $DSS(G)$ of a graph $G$ is a square matrix of order equal to the order of $G$ with its $(i,j)^{th}$ entry as ${{d_i}^{2}+{d_j}^{2}}$ if $i\neq j$ and zero otherwise, where $d_i$ is the degree of the $i^{th}$ vertex of $G$. In this paper, we obtain the characteristic polynomial of the degree square sum matrix of graphs obtained by some graph operations. In addition, bounds for largest degree square sum eigenvalue and for degree square sum energy of graphs are obtained.