论文标题
线性表示的线图的非几何表光谱序列
Non-Geometric Cospectral Mates of Line Graphs with a Linear Representation
论文作者
论文摘要
为了发生发病率的几何$ \ MATHCAL {g} =（\ Mathcal {p}，\ Mathcal {l}，\ text {i}）$，\ text {i}）$ $ \ mathcal {t} _n _n^*（\ nron-non-non-draph in-Graph in-Graph cors optral in-Graph in-graph non-cortrrict $ \ $ \ MATHCAL {G} $的$γ$。 作为一个应用程序，我们表明，对于$ h \ geq 2 $和$ 0 <m <h $，有强烈的常规图，带有参数$（v，k，λ，μ）=（2^{2H}（2^{2^{m+h}+2^m-2^h），2^h+1），2^h+1） （2^m-1））$不是订单$（s，t，α）的部分几何形状的点图=（（2^h+1）（2^m-1），2^h-1，2^m-1）$。
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 $(s,t,α) = ((2^h+1)(2^m-1), 2^h-1, 2^m-1)$.
