Switched symplectic graphs and their 2-ranks

Aida Abiad, Willem H. Haemers

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)

Abstract

We apply Godsil–McKay switching to the symplectic graphs over F2 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 2 ν+ 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 - 1 Oct 2016
Externally publishedYes

Keywords

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

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