Square of a graph

Square of a graph --- квадрат графа.

The square of a graph [math]\displaystyle{ G^{2} }[/math] is the graph with a vertex set [math]\displaystyle{ V(G^{2}) = V(G) }[/math], for which [math]\displaystyle{ (u,v) }[/math] is an edge in [math]\displaystyle{ G^{2} }[/math] if and only if the distance [math]\displaystyle{ d_{G}(u,v) }[/math] between [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] is 1 or 2. It is known that the square of every 2-connected graph is hamiltonian and the square of a connected graph is pseudo-hamiltonian.