Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1

W.H. Haemers, Q. Xiang

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Abstract

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integer m. If m > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 +m2,m4 +m2,m4 +m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by Gutman) among all graphs on 4m4 vertices. For odd m>3 the strongly regular graphs seem to be new.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages9
Volume2008-86
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-86

Keywords

  • Cayley graph
  • difference set
  • energy of a graph
  • Hadamard matrix
  • regular Hadamard matrix
  • strongly regular graph
  • Seidel switching.

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