具有线性表示的线图的非几何共谱偶
Non-Geometric Cospectral Mates of Line Graphs with a Linear Representation
摘要：
对于具有线性表示$\mathcal{T}_n^*(\mathcal{K})$的入射几何$\mathcal{G} = (\mathcal{P}, \mathcal{L}, \text{I})$，我们应用WQH转换来构造非几何图$Γ'$与$\mathcal{G}$的线图$Γ$共谱。作为一个应用，我们证明了对于$h \geq 2$和$0 < m < h$，存在带参数$(v, k, λ, μ) = (2^{2h} (2^{m+h}+2^m-2^h), 2^h (2^h+1)(2^m-1), 2^h (2^{m+1}-3), 2^h (2^m-1))$的强正则图不是$(s,t,α) = ((2^h+1)(2^m-1), 2^h-1, 2^m-1)$阶部分几何的点图.
英文摘要：
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 $Γ'$ cospectral with the line graph $Γ$ of $\mathcal{G}$. As an application, we show that for $h \geq 2$ and $0 < m < h$, there are strongly regular graphs with parameters $(v, k, λ, μ) = (2^{2h} (2^{m+h}+2^m-2^h), 2^h (2^h+1)(2^m-1), 2^h (2^{m+1}-3), 2^h (2^m-1))$ which are not point graphs of partial geometries of order $(s,t,α) = ((2^h+1)(2^m-1), 2^h-1, 2^m-1)$.
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