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In this paper, we study partial automorphisms and, more generally, injectivepartial endomorphisms of a finite undirected path from Semigroup Theoryperspective. Our main objective is to give formulas for the ranks of themonoids $IEnd(P_n)$ and $PAut(P_n)$ of all injective partial endomorphisms andof all partial automorphisms of the undirected path $P_n$ with $n$ vertices. Wealso describe Green's relations of $PAut(P_n)$ and $IEnd(P_n)$ and calculatetheir cardinals.

Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path