Green's relations on the strong endomorphism monoid of a graph
An endomorphism of a graph is called strong if in addition to preserving edges it also reflects edges. The author describes inside the graph Green's relations \(\mathcal L\), \(\mathcal R\), \(\mathcal H\) and \(\mathcal D\) for pairs of strong graph endomorphisms. As a consequence the author proves that the monoid of strong endomorphisms \(S\text{ End}(G)\) is regular. The methods are used to construct \(u \in S \text{ End}(G)\) with \(uf = g\) for \(f,g \in S \text{ End}(G)\) with \((f,g) \in {\mathcal L}\). All graphs are finite and undirected.
scientific article; zbMATH DE number 436439