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.