Strongly Regular Graphs with Maximal Energy

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Abstract

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
Volume2007-37
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-37

Keywords

  • Graph energy
  • Strongly regular graph
  • Hadamard matrix.

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    Haemers, W. H. (2007). Strongly Regular Graphs with Maximal Energy. (CentER Discussion Paper; Vol. 2007-37). Operations research.