摘要
本文讨论奇阶完备残差图,证明了对于任意奇数n,不存在奇阶K_n-残差图.对任意奇数t≥3和n=2t,2t-2,2t-4构造了一类具有奇阶2n+t的K_n-残差图.我们证明了当n≡0(mod4)时,K_n-残差图的最小奇阶为5n/2+1;当n≡2(mod4)时,K_n-残差图的最小奇阶为5n/2,并且证明了相应的最小奇阶K_n-残差图的唯一性.
In this paper, we discuss residually complete graphs with odd order, it is easy to prove that for any odd number n, there is no Kn-residual graphs with odd order. For odd integer t ≥3 and n = 2t, 2t - 2, 2t - 4, we construct a class of Kn-residual graphs with odd order 2n ＋ t. For every even number n, we proved that there exist Kn-residual graphs with odd orders are 5n/2 and 5n/2 ＋ 1 whenever n ≡2 （rnod 4） and n ≡ 0 （mod 4）respectively. For n ≡ 2 （mod 4）, we proved that Kn-residual graph with least odd order is unique.
出处
《应用数学学报》
CSCD
北大核心
2011年第5期778-785,共8页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金资助项目(1097118)
关键词
完备残差图
闭邻域
residually complete graph
neighborhood
