Abstract
Let G be a simple graph of order n, without isolated vertices. Denote by A = (a(ij))(nxn) the adjacency matrix of G. Eigenvalues of the matrix A, lambda(1) >= lambda(2) >= ... >= lambda(n), form the spectrum of the graph G. An important spectrum-based invariant is the graph energy, defined as E(G) = Sigma(n)(i=1) vertical bar lambda(i)vertical bar. The determinant of the matrix A can be calculated as det A = Pi(n)(i=1) lambda(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 vertical bar det A vertical bar are derived. Consequently, all the bounds established in the aforementioned paper are improved.