Vertex splitting

Vertex splitting --- расщепление вершины.

A vertex splitting of a digraph [math]\displaystyle{ G }[/math] is achieved by replacing a vertex [math]\displaystyle{ v_{0} }[/math] of [math]\displaystyle{ G }[/math] by two new vertices [math]\displaystyle{ v_{i} }[/math] and [math]\displaystyle{ v_{j} }[/math], replacing each arc [math]\displaystyle{ v_{0} \rightarrow v_{x} }[/math] in [math]\displaystyle{ G }[/math] by [math]\displaystyle{ v_{j} \rightarrow v_{x} }[/math], replacing each arc [math]\displaystyle{ v_{x} \rightarrow v_{0} }[/math] in [math]\displaystyle{ G }[/math] by [math]\displaystyle{ v_{x} \rightarrow v_{i} }[/math], and adding the arc [math]\displaystyle{ v_{i} \rightarrow v_{j} }[/math].