Some new bounds for the energy of graphs☆

Let G be a graph with n vertices and m edges. The energy of a graph G is defined as the sum of absolute values of the eigenvalues about its adjacency matrix, i.e. s(G) = & sum;ni=1 |)i|. In this paper, we derive some new upper bounds on the graph energy based on a new formula and some inequalities for calculating the graph energy, and characterize the extremal graphs. In addition, we propose some new lower bounds for the graph energy involving order n, the size m, the eigenvalue with maximum absolute value )1 and the eigenvalue with minimum absolute value )n of the graph G, and characterize the extremal graphs. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.