2019/04/07 by Ihringer, Ferdinand, Munemasa, Akihiro · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1904.03680
We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n, 2), O(n, 3), O(n, 5), O+(n, 3), and O-(n, 3) are not determined by its parameters for n ≥ 6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.