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A rectangular group is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. Some special cases of rectangular groups consisting of left groups and right groups are also considered here. Let $$ \mathrm {Cay}(S,A) $$ Cay(S,A) denote the Cayley digraph of the rectangular group S with the connection set A. In this paper, we are interested in studying some properties...
We determine the number of locally strong endomorphisms of directed and undirected paths—direction here is in the sense of a bipartite graph from one partition set to the other. This is done by the investigation of congruence classes, leading to the concept of a complete folding, which is used to characterize locally strong endomorphisms of paths. A congruence belongs to a locally strong endomorphism...
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