Switched symplectic graphs and their 2-ranks
Abiad,Aida Haemers,W. H.
Abiad,Aida
Haemers,W. H.
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 (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 .
Description
Date
2016
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Volume Title
Publisher
Research Projects
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Keywords
strongly regular graph, symplectic graphs, switching, 2-rank, Hadamard matrix
Citation
Abiad, A & Haemers, W H 2016, 'Switched symplectic graphs and their 2-ranks', Designs Codes and Cryptography, vol. 81, no. 1, pp. 35-41. https://doi.org/10.1007/s10623-015-0127-x
License
info:eu-repo/semantics/openAccess