  In 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 the
monoids $IEnd(P_n)$ and $PAut(P_n)$ of all injective partial endomorphisms and
of all partial automorphisms of the undirected path $P_n$ with $n$ vertices. We
also describe Green's relations of $PAut(P_n)$ and $IEnd(P_n)$ and calculate
their cardinals.
