Bounds for Degree-Sum adjacency eigenvalues of a graph in terms of Zagreb indices

Abstract

For a graph $G$ the degree sum adjacency matrix $DS_A(G)$ is defined as a matrix, in which every element is sum of the degrees of the vertices if and only if the corresponding vertices are adjacent, otherwise it is zero. In this paper we obtain the bounds for the spectral radius and partial sum of the eigenvalues of the $DS_A$ matrix. We also find the bounds for the $DS_A$ energy of a graph in terms of its Zagreb indices.

Keywords

• adjacency eigenvalues
• degree sum adjacency matrix
• zagreb index
• eigenvalues
• energy