Strongly Regular Graphs with Maximal Energy

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The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages7
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper


  • Graph energy
  • Strongly regular graph
  • Hadamard matrix.


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