On energy and Laplacian energy of bipartite graphs

摘要

Let G be a bipartite graph of order it with in edges. The energy epsilon(G) of G is the sum of the absolute values of the eigenvalues of the adjacency matrix A. In 1974, one of the present authors established lower and upper bounds for epsilon(G) in terms of 11, in, and detA. Now, more than 40 years later, we correct some details of this result and determine the extremal graphs. In addition, an upper bound on the Laplacian energy of bipartite graphs in terms of n, m, and the first Zagreb index is obtained, and the extremal graphs characterized. (C) 2015 Elsevier Inc. All rights reserved.