Maximal energy graphs

Given a graph G, its energy E(G) is defined as the sum of the absolute valu es of the eigenvalues of G. The concept of the energy of a graph was introd uced in the subject of chemistry by I. Gutman. due to its relevance to the total pi -elrctron energy of certain molecules. In this paper, we show that if G is a graph on n vertices, then E(G) less than or equal to (n/2)(1 + r ootn) must hold, and we give an infinite family of graphs for which this bo und is sharp. (C) Academic Press.