A note on the relationship between graph energy and determinant of adjacency matrix.

Let G be a simple graph of order n , without isolated vertices. Denote by A = (a i j) n × n the adjacency matrix of G. Eigenvalues of the matrix A , λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n , form the spectrum of the graph G. An important spectrum-based invariant is the graph energy, defined as E (G) = ∑ i = 1 n | λ i |. The determinant of the matrix A can be calculated as det A = ∏ i = 1 n λ i . Recently, Altindag and Bozkurt [Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem.77 (2017) 9–14] improved some well-known bounds on the graph energy. In this paper, several inequalities involving the graph invariants E (G) and | det A | are derived. Consequently, all the bounds established in the aforementioned paper are improved. [ABSTRACT FROM AUTHOR]