广义Paley图的团和染色及同步方法
Cliques and colorings in generalized Paley graphs and an approach to synchronization
摘要：
给定一个有限域，如果两个顶点的差位于乘法群的一个固定子群中，则可以用域元素作为顶点并连接两个顶点构成有向图。如果-1包含在这个固定子群中，那么我们得到一个无向图，称为广义Paley图。本文研究团数和色数一致的广义Paley图，并将这一理论与一维本原仿射置换群的同步性研究联系起来。
英文摘要：
Given a finite field, one can form a directed graph using the field elements as vertices and connecting two vertices if their difference lies in a fixed subgroup of the multiplicative group. If -1 is contained in this fixed subgroup, then we obtain an undirected graph that is referred to as a generalized Paley graph. In this paper we study generalized Paley graphs whose clique and chromatic numbers coincide and link this theory to the study of the synchronization property in 1-dimensional primitive affine permutation groups.
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