Detour distance

Detour distance --- расстояние обхода.

Let [math]\displaystyle{ G }[/math] be a nontrivial connected graph. For distinct vertices [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] of [math]\displaystyle{ G }[/math], the detour distance [math]\displaystyle{ D(u,v) }[/math] between [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math] is the length of the longest [math]\displaystyle{ u-v }[/math] path in [math]\displaystyle{ G }[/math]. Thus [math]\displaystyle{ 1 \leq D(u,v) \leq n-1 }[/math], where [math]\displaystyle{ D(u,v) = 1 }[/math] if and only if [math]\displaystyle{ uv }[/math] is a bridge of [math]\displaystyle{ G }[/math] and [math]\displaystyle{ D(u,v) = n-1 }[/math] if and only if [math]\displaystyle{ G }[/math] contains a hamiltonian [math]\displaystyle{ u-v }[/math] path.