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- Partial automorphisms and injective partial endomorphisms of a finite undirected pathPublication . Dimitrova, Ilinka; Fernandes, V. H.; Koppitz, J.; Quinteiro, TeresaIn this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of themonoids IEnd(P-n) and PAut(P-n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path Pn with n vertices. We also describe Green's relations of PAut(P-n) and IEnd(P-n) and calculate their cardinals.