Regular Article: Maximal Energy Graphs

  • Authors:

  • Jack H. Koolen;Vincent Moulton

  • Affiliations:

  • FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501, Bielefeld, Germanyf1jkoolen@mathematik.uni-bielefeld.def1;Department of Physics and Mathematics (FMI), Mid Sweden University, Sundsvall, S 851-70, Swedenf2vince@dirac.fmi.mh.sef2

  • Venue:
  • Advances in Applied Mathematics
  • Year:
  • 2001

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Abstract

Given a graph G, its energyE(G) is defined as the sum of the absolute values of the eigenvalues of G. The concept of the energy of a graph was introduced in the subject of chemistry by I. Gutman, due to its relevance to the total @p-electron energy of certain molecules. In this paper, we show that if G is a graph on n vertices, then E(G)@?n21+n must hold, and we give an infinite family of graphs for which this bound is sharp.