图的弱自同态幺半群

Weak Endomorphism Monoid of a Graph

定义了图的弱自同态,证明了一个图的所有弱自同态在映射的合成下可以构成一个幺半群,刻画了图的弱自同态幺半群的两类格林关系(L关系和R关系)。通过L关系给出了其每个L类中都包含幂等元的条件。最后,给出了图的弱自同态幺半群是正则半群的充分必要条件。

In this paper,the weak endomorphism of a graph was defined.It is proved that the set of all weak endomorphisms of a graph can form a monoid.The Green ' s relation of these monoids is described.The conditions are given under which every L-class of the weak endomorphism monoid of a graph contains a idempotent.The conditions are got under which the weak endomorphism monoid of a graph is regular.