Energy of Nonsingular Graphs: Improving Lower Bounds

Abstract

Let $G$ be a simple graph of order $n$ and $A$ be its adjacency matrix. Let ${\lambda }_1\ge {\lambda }_2\ge \dots \ge {\lambda }_n$ be eigenvalues of matrix $A$ . Then, the energy of a graph $G$ is defined as $\epsilon \left(G\right)={\displaystyle {\sum }_{i=1}^n\left|{\lambda }_i\right|}$ . In this paper, we will discuss the new lower bounds for the energy of nonsingular graphs in terms of degree sequence, 2-sequence, the first Zagreb index, and chromatic number. Moreover, we improve some previous well-known bounds for connected nonsingular graphs.