中文摘要：

本文研究了任意维超平面完备残差图和多重超平面完备残差图,将Erd?os、Harary和Klawe's定义的平面残差图推广到任意维超平面.利用容斥原理以及集合的运算性质等方法,获得了任意维超平面完备残差图的最小阶和唯一极图,以及任意维超平面完备残差图的一个重要性质,同时获得了多重任意维超平面完备残差图的最小阶和唯一极图.

英文摘要：

In this paper,we study any number of dimensions hyperplane complete residual graphs and multiply any number of dimensions hyperplane complete residual graphs,and extend Erd?os,Harary and Klawe's definition of plane complete residual graph to hyperplane and obtain dimensions hyperplane complete residual graph.With the method of including excluding principle and set operation,we obtain the minimum order of any number of dimensions hyperplane complete residual graphs and a unique minimal any number of dimensions hyperplane complete residual graph,and an important property of any number of dimensions hyperplane complete residual graph.In addition,we obtain the minimum order of multiply any number of dimensions hyperplane complete residual graphs and a unique minimal multiply any number of dimensions hyperplane complete-residual graphs.