图的[强]自同态摹群

(Strong) Endomorphism Monoids of the Graphs

进一步讨论诸如积图、临界图、字典序积等一些图的 [强 ]自同态摹群 ,并在一定的条件下完全确定了相应的摹群 ,发现临界图以及两个临界图的联图均为E A不可收缩图 ,证明了积图的自同态摹群与图的自同态摹群的积相等的一个充要条件 ,以及关于S A不可收缩图的一个充要条件 。

WT5BZ]The endomorphism monoids of some graphs such as the critical graphs, the product or lexicographical product of two graphs are further discussed, and some of these monoids are completely determined in proper conditions. It is discovered that the critical graphs and the join of two critical graphs are E?A unretractable respectively. Two necessary sufficient conditions are proved, one of which is for that the endomorphism monoid of the product of two graphs is equal to the product of the endomorphism monoids of the two graphs, and the other is for the S?A unretractable graphs. At last, a group congruence is given on the endomorphism monoid of the lexicographical product of two graphs.