关于图的弱核和伪核

摘要

A graph G is a core if every endomorphism of G is an automorphism.A graph G is called a weak—core (resp.pseudo—core) if every endomorphism of G is either an automorphism or the image of the endo—morphism being a core (resp.maximum clique) of G.Since the concept of weak—core (pseudo——core) is the most close to the core, it is a meaningful problem whether a graph is a weak—core (pseudo—core) or not.Inthis paper We give some necessary and sufficient conditions and examples for weak—core (pseudo—core).%如果图G的每个自同态都是自同构,则称G为一个棱.如果图G的每个自同态都是自同构或者自同态的象集是一个核(最大团),则称G为一个弱核(伪棱).因为弱核(伪核)的概念最接近于核,判别一个图是否为弱核(伪核)是有意义的问题.我们给出一个图是弱棱(伪核)的充要条件和弱核(伪核)的一些例子.