论文标题
在平方秩序的广义佩利图上
On eigenfunctions and maximal cliques of generalised Paley graphs of square order
论文作者
论文摘要
令GP $（q^2，m）$为有限字段上定义的$ m $ paley图，并使用$ q^2 $。我们在广义Paley Graphs gp $（q^2，m）$中研究本征函数和最大集团，其中$ m \ mid（q+1）$。特别是，我们明确地构造了$ \ frac {q+1} {m} $或$ \ frac {q+1} {m} {m} {m} {m}+1 $ 1 $（q^2，m）$中的最大列，并显示重量分发的eigenfunuction smill eigenfunv for the eigenfunv in $ - \ frac {q+1} {m} $ gp $（q^2，m）$。这些新结果扩展了Baker等人的工作。 Al and Goryainov等。在平方顺序的Paley图上。我们还研究了gp $（q^2，m）$的ERDőS-KO-RADO定理的稳定性（Sziklai首先证明）。
Let GP$(q^2,m)$ be the $m$-Paley graph defined on the finite field with order $q^2$. We study eigenfunctions and maximal cliques in generalised Paley graphs GP$(q^2,m)$, where $m \mid (q+1)$. In particular, we explicitly construct maximal cliques of size $\frac{q+1}{m}$ or $\frac{q+1}{m}+1$ in GP$(q^2,m)$, and show the weight-distribution bound on the cardinality of the support of an eigenfunction is tight for the smallest eigenvalue $-\frac{q+1}{m}$ of GP$(q^2,m)$. These new results extend the work of Baker et. al and Goryainov et al. on Paley graphs of square order. We also study the stability of the Erdős-Ko-Rado theorem for GP$(q^2,m)$ (first proved by Sziklai).
