Switched symplectic graphs and their 2-ranks

A. Abiad Monge, W. Haemers

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

We apply Godsil-McKay switching to the symplectic graphs over F 2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graph with parameters (2 2ν −1,2 2ν−1 ,2 2ν−2 ,2 2ν−2 ) and 2-rank 2ν+2 when ν≥3 . For the symplectic graph on 63 vertices we investigate repeated switching by computer and find many new strongly regular graphs with the above parameters for ν=3 with various 2-ranks. Using these results and a recursive construction method for the symplectic graph from Hadamard matrices, we obtain several graphs with the above parameters, but different 2-ranks for every ν≥3 .
Original languageEnglish
Pages (from-to)35-41
Number of pages7
JournalDesigns CoDes and Cryptography
Volume81
Issue number1
DOIs
Publication statusPublished - Oct 2016

Keywords

  • Strongly regular graph
  • Symplectic graphs
  • Switching
  • 2-Rank
  • Hadamard matrix

Cite this

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abstract = "We apply Godsil-McKay switching to the symplectic graphs over F 2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graph with parameters (2 2ν −1,2 2ν−1 ,2 2ν−2 ,2 2ν−2 ) and 2-rank 2ν+2 when ν≥3 . For the symplectic graph on 63 vertices we investigate repeated switching by computer and find many new strongly regular graphs with the above parameters for ν=3 with various 2-ranks. Using these results and a recursive construction method for the symplectic graph from Hadamard matrices, we obtain several graphs with the above parameters, but different 2-ranks for every ν≥3 .",
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Switched symplectic graphs and their 2-ranks. / Abiad Monge, A.; Haemers, W.

In: Designs CoDes and Cryptography, Vol. 81, No. 1, 10.2016, p. 35-41.

Research output: Contribution to journalArticleAcademicpeer-review

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N2 - We apply Godsil-McKay switching to the symplectic graphs over F 2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graph with parameters (2 2ν −1,2 2ν−1 ,2 2ν−2 ,2 2ν−2 ) and 2-rank 2ν+2 when ν≥3 . For the symplectic graph on 63 vertices we investigate repeated switching by computer and find many new strongly regular graphs with the above parameters for ν=3 with various 2-ranks. Using these results and a recursive construction method for the symplectic graph from Hadamard matrices, we obtain several graphs with the above parameters, but different 2-ranks for every ν≥3 .

AB - We apply Godsil-McKay switching to the symplectic graphs over F 2 with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new strongly regular graph with parameters (2 2ν −1,2 2ν−1 ,2 2ν−2 ,2 2ν−2 ) and 2-rank 2ν+2 when ν≥3 . For the symplectic graph on 63 vertices we investigate repeated switching by computer and find many new strongly regular graphs with the above parameters for ν=3 with various 2-ranks. Using these results and a recursive construction method for the symplectic graph from Hadamard matrices, we obtain several graphs with the above parameters, but different 2-ranks for every ν≥3 .

KW - Strongly regular graph

KW - Symplectic graphs

KW - Switching

KW - 2-Rank

KW - Hadamard matrix

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