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