Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp. © 2003 Elsevier Inc. All rights reserved.
Rada, J., & Tineo, A. (2004). Upper and lower bounds for the energy of bipartite graphs. Journal of Mathematical Analysis and Applications, 289(2), 446–455. https://doi.org/10.1016/j.jmaa.2003.08.027