系统的核与核度理论(V)——系统和补系统的关系

THE CORE AND CORITIVITY OF A SYSTEM(Ⅴ)——RELATIONS BETWEEN A SYSTEM AND ITS COMPLEMENT

本文主要研究了网络的最大度△与它的核度h之间的相互关系,由此讨论了核度Nordaus-Gaddum的积的形式,获得了在最大度数给定条件下,具有最大最小核度的树型网络结构及其相应的构造,树与补树的Nordaus-Gaddum问题,由此对于一般简单网络的情况进行了研究,并对Nordaus-Gaddum问题积的形式提出了猜想。

The basic properties and network structure on cortivity are studied in this paper. The structure and construction with maximum and minimum coritivity of a tree and its complement are obtained. The Nordaus-Gaddhum problem of a tree and its complement is discussed. Furthermore, the Nordaus-Gaddhum problem of general network is studied, and the conjecture of product form of Nordaus-Gaddhum problem for general network is proposed.