Strong) Endomorphism Monoids of the Graphs
Zhu Yong · Journal of Yantai University · 2000
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.