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