More on borderenergetic graphs

Abstract

© 2016 Elsevier Inc. All rights reserved. The energy 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 Kn, i.e., if 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.