Reconstructible graph

Reconstructible graph --- реконструируемый граф.

1. A graph [math]\displaystyle{ G }[/math] is reconstructible, if every graph hypomorphic to [math]\displaystyle{ G }[/math] is isomorphic to [math]\displaystyle{ G }[/math].

2. An infinite locally finite connected graph [math]\displaystyle{ G }[/math] is reconstructible, if there exists a finite family [math]\displaystyle{ (\Omega_{i})_{0\leq i \lt n} }[/math] ([math]\displaystyle{ n \geq 2 }[/math]) of pairwise finitely separable subsets of its end set [math]\displaystyle{ {\mathcal E}(G) }[/math] such that, for all [math]\displaystyle{ x,y,x',y' \in V(G) }[/math] and every isomorphism [math]\displaystyle{ f }[/math] of [math]\displaystyle{ G - \{x,y\} }[/math] onto [math]\displaystyle{ G - \{x',y'\} }[/math], there is a permutation [math]\displaystyle{ \pi }[/math] of [math]\displaystyle{ \{0, \ldots, n-1\} }[/math] such that [math]\displaystyle{ f(\Omega_{i}) = \Omega_{\pi(i)} }[/math] for [math]\displaystyle{ 0 \leq i \lt n }[/math].