The monoid of strong endomorphisms of a graph
The author investigates strong endomorphisms of finite undirected graphs without loops and multiple edges. A strong endomorphism is a mapping on the vertex set which preserves and reflects edges (i.e. the preimage of an edge is an edge). The author studies Green's \(\mathcal R\) and \(\mathcal L\) classes of the monoids of strong endomorphisms. He describes idempotents in these classes and all inverses to any strong endomorphism taking into account that the monoid of strong endomorphisms is always regular, i.e. inverses in this sense do exist. He also gives formulas for the number of idempotents and inverses.
scientific article; zbMATH DE number 638349