有限域上仿射m面诱导的图Ⅰ(英文)

The Graph Induced by Affine m-Flats over Finite Fields I

设IFq 是具有q个元素的有限域 ,其中q是一个素数的幂。由IFq 上n维仿射空间AG(n ,IFq)的m面诱导的图г被研究。特别 ,г中任两个顶点间的距离通过它们的联的维数被确定 。

Let IF q be the finite field with q elements,where q is a power of a prime.The graph γ induced by m-flats of n-dimensional affine space AG(n,IF q)over IF q is studied.In particular,the distance between any two vertices in γ is determined by means of dimension of their join,and the neighborhood of any vertex in γ is given in a explicit form.