有限有向图与有限幂零半群

THE FINITE DIGRAPH AND FINITE NILPOTENT

本文给有限有向图Ｄ定义了乘法，从而得到这个有向图确定的半群Ｓ，证明了Ｓ的最小生成集Ａ＝Ｓ－Ｓ２＝Ｖ（Ｄ的顶点集）且，这个半群的秩等于Ｄ的顶点的个数。证明了两个有限有向图同构，当且仅当，它们分别确定的半群同构。

n this peper we give a operation as multiPOlication to finite digraph D,obtain a finite nilPOtentsemigroup S, and show that,the minimum generated set of S is A=S-S2,is venices set of D. PL', (in which L is a structure set of S,L *=A+-L,L. is a ideal of A+,PL* is a Rees--Congruence)and show two finite digraph D1, D2 are isomoorphism,if and only if,SIMSZ (where SI, SZ -- are finitenilpotent semigroup, They are obtain from D1 .D2 ).