successive minima

In this paper,the authors discussed connected residually complete graphs,determined the third minimal order of connected K_2residual graphs,for n≠2 the weak minimal order of connected K_n-residual graphs,that ismin{v(G)｜G is connected K_n-residual graph,v(G)>2n+2}=2n+3,n=2,4,62n+4,n≠2,4,6and constructed the corresponding graphs.

讨论连通的残差完备图,确定了连通的K2残差图的第二个最小阶及n≠2时,连通的Kn残差图的次最小阶,即min{v(G)|G是连通的Kn残差图,v(G)>2n+2}=2n+3,n=2,4,62n+4,n≠2,4,6并且构造了对应的残差完备图;同时证明了n=6时,C5[K3]是唯一的2n+3阶的连通Kn残差图,还对任意正整数n和k,构造了具有2n+2k阶的残差完备图。