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Graphs and Combinatorics

, Volume 19, Issue 1, pp 131–135 | Cite as

Maximal Energy Bipartite Graphs

  • Jack H. Koolen
  • Vincent Moulton

Abstract.

 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.

Keywords

Bipartite Graph 
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Copyright information

© Springer-Verlag Tokyo 2003

Authors and Affiliations

  • Jack H. Koolen
    • 1
  • Vincent Moulton
    • 2
  1. 1.FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501 Bielefeld, Germany. e-mail: jkoolen@mathematik.uni-bielefeld.deDE
  2. 2.Physics and Mathematics Department (FMI), Mid Sweden University, Sundsvall, S 851-70, Sweden. e-mail: vince@dirac.fmi.mh.seSE

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