中文摘要：

利用幂等元刻画了自同态正则分裂图的自同态幺半群的ρf类和自同态像的个数，进而得到了 类及R己类的个数．

英文摘要：

The endomorphism monoid of a graph is a very important research aspect in algebraic graph. A split graph is called End-regular i[ its endomorphism monoid is regular. The endomorphism monoid End X o{ the End-regular split graph X to reveal the algebraic structure of End X is studied. By discussing the Green＇s equivalences of End X, the number of the idempotents and the ρf classes of End X, and characterize the image of endomorphism of End X are gat. At last, the number of classes and R classes of End X are obtained, respectively.