Maximal Energy Bipartite Graphs

 Given a graph G, its energy E(G) is defined to be the sum of the absolute values of the eigenvalues of G. This quantity is used in chemistry to approximate the total π-electron energy of molecules and in particular, in case G is bipartite, alternant hydrocarbons. Here we show that if G is a bipartite graph with n vertices, then must hold, characterize those bipartite graphs for which this bound is sharp, and provide an infinite family of maximal energy bipartite graphs. Received: December 1, 2000 Final version received: August 28, 2001 RID="*" ID="*" The author thanks the Swedish Natural Science Research Council (NFR) – grant M12342-300 – for its support. Acknowledgments. The authors would like to thank Ivan Gutman for encouraging them to write this paper, and for helpful discussions on this topic. They also would like to thank Edwin van Dam for his reference concerning connected bipartite regular graphs with four eigenvalues.