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

W.H. Haemers, Q. Xiang

Research output: Working paperDiscussion paperOther research output

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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

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Strongly Regular Graph
Hadamard Matrix
Difference Set
Graph in graph theory
Energy
Odd
Integer

Keywords

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

Cite this

Haemers, W. H., & Xiang, Q. (2008). Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1. (CentER Discussion Paper; Vol. 2008-86). Tilburg: Operations research.
Haemers, W.H. ; Xiang, Q. / Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1. Tilburg : Operations research, 2008. (CentER Discussion Paper).
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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.",
keywords = "Cayley graph, difference set, energy of a graph, Hadamard matrix, regular Hadamard matrix, strongly regular graph, Seidel switching.",
author = "W.H. Haemers and Q. Xiang",
note = "Subsequently published in European Journal of Combinatorics, 2010 Pagination: 9",
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language = "English",
volume = "2008-86",
series = "CentER Discussion Paper",
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Haemers, WH & Xiang, Q 2008 'Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1' CentER Discussion Paper, vol. 2008-86, Operations research, Tilburg.

Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1. / Haemers, W.H.; Xiang, Q.

Tilburg : Operations research, 2008. (CentER Discussion Paper; Vol. 2008-86).

Research output: Working paperDiscussion paperOther research output

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KW - difference set

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KW - regular Hadamard matrix

KW - strongly regular graph

KW - Seidel switching.

M3 - Discussion paper

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Haemers WH, Xiang Q. Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1. Tilburg: Operations research. 2008. (CentER Discussion Paper).