Sharp upper bounds for total π-electron energy of alternant hydrocarbons

The energy E( G) of a graph G is defined as the sum of the absolute values of all the eigenvalues of the adjacency matrix of the graph G. This quantity is used in chemistry to approximate the total pi- electron energy of molecules and in particular, in case G is bipartite, alternant hydrocarbons. In this paper, we show that if G = ( V-1, V-2; E) is a bipartite graph with m >= n(1) edges and broken vertical bar V-1 broken vertical bar = n(1) >= n(2) = broken vertical bar V-2 broken vertical bar, then [GRAPHICS] and [GRAPHICS] must hold.