Energy of Nonsingular Graphs: Improving Lower Bounds

Abstract

Let G be a simple graph of order n and A be its adjacency matrix. Let λ1≥λ2≥…≥λn be eigenvalues of matrix A. Then, the energy of a graph G is defined as εG=∑i=1nλi. 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.