More on borderenergetic graphs

The energy E(G)E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. If a graph G of order n   has the same energy as the complete graph KnKn, i.e., if E(G)=2(n−1)E(G)=2(n−1), then G is said to be borderenergetic. We obtain three asymptotically tight bounds on the edge number of borderenergetic graphs. Then, by using disconnected regular graphs we construct connected non-complete borderenergetic graphs.