In this paper, we characterize the structure of the weakly endomorphism monoids of graphs. Furthermore, we present the necessary andlsufficient conditions for,a weakly endomorphism to he a regu- lar element.%刻画了图的弱自同态幺半,群的结构,通过刻画图的弱自同态幺半群的格林关系,给出了弱自同态是正则元的充分必要条件.
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