由仿射线诱导的图的次成分Ⅰ

摘要

Let Fq be a finite field with q elements, and,AG(n, Fq) be the n-dimensional affine space over Fq. The subconstituent Г(α) of the graph Г induced by lines of AG(n,Fq) is studied for any vertex α of Г. In particular, it is shown that Г(α) is regular if and only if n=2.%设Fq是一个含有q个元素的有限域,AG(n,Fq)是Fq上的n维仿射空间,Г是由AG(n,Fq)中的仿射线诱导的图.对于Г的任一个顶点α,次成分Г(α)被研究.这里特别指出:Г(α)是正则图当且仅当n=2.