2014/12/09 by Aida Abiad, Abiad, Aida, Willem H. Haemers +1
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1412.2945
openalex publication_date 2014/12/09 · arxiv created 2015/07/27 · arxiv updated 2015/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply Godsil-McKay switching to the symplectic graphs over \mathbbF2 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 (22ν -1, 22ν-1, 22ν-2,22ν-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.