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 language | English |
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Pages (from-to) | 35-41 |
Number of pages | 7 |
Journal | Designs, Codes and Cryptography |
Volume | 81 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Oct 2016 |
Externally published | Yes |
Keywords
- 2-Rank
- Hadamard matrix
- Strongly regular graph
- Switching
- Symplectic graphs