For an incidence geometry $\mathcal{ G} = (\mathcal{ P}, \mathcal{ L}, \text{ I})$ with a linear representation $\mathcal{ T}_n^*(\mathcal{ K})$, we apply WQH switching to construct a non-geometric graph $\Gamma'$ cospectral with the line graph $\Gamma$ of $\mathcal{ G}$. As an application, we show that for $h \geq 2$ and $0 < m < h$, there are strongly regular graphs with parameters $(v, k, \lambda, \mu) = (2^{ 2h} (2^{ m+h}+2^m-2^h), 2^h (2^h+1)(2^m-1), 2^h (2^{ m+1}-3), 2^h (2^m-1))$ which are not point graphs of partial geometries of order $(s,t,\alpha) = ((2^h+1)(2^m-1), 2^h-1, 2^m-1)$.
Categories: math.CO