K-reconstructible graph

[math]\displaystyle{ k }[/math]-reconstructible graph --- [math]\displaystyle{ k }[/math]-реконструируемый граф.

Let [math]\displaystyle{ k }[/math] be an integer ([math]\displaystyle{ k \geq 1 }[/math]) and [math]\displaystyle{ G = (V,E) }[/math] a graph with more than [math]\displaystyle{ k }[/math] vertices, a graph [math]\displaystyle{ G' = (V,E') }[/math] is a [math]\displaystyle{ k }[/math]-reconstuction of [math]\displaystyle{ G }[/math] if, for any subset [math]\displaystyle{ W }[/math] of [math]\displaystyle{ V }[/math] with [math]\displaystyle{ k }[/math] elements, the subgraph [math]\displaystyle{ G(W) }[/math] and [math]\displaystyle{ G'(W) }[/math] induced by [math]\displaystyle{ W }[/math] are isomorphic. The graph [math]\displaystyle{ G }[/math] is [math]\displaystyle{ k }[/math]-reconstructible, when each [math]\displaystyle{ k }[/math]-reconstruction of [math]\displaystyle{ G }[/math] is isomorphic to [math]\displaystyle{ G }[/math]. G. Lopez (1978) proved that any graph is 6-reconstructible.