Lexicographic product

Lexicographic product --- лексикографическое произведение, композиция графов.

Given graphs [math]\displaystyle{ G }[/math] and [math]\displaystyle{ H }[/math], the lexicographic product [math]\displaystyle{ G[H] }[/math] has a vertex set [math]\displaystyle{ \{(g,h): g \in V(G), \; h \in V(H)\} }[/math] and two vertices [math]\displaystyle{ (g,h), (g',h') }[/math] are adjacent if and only if either [math]\displaystyle{ (g,g') }[/math] is an edge of [math]\displaystyle{ G }[/math] or [math]\displaystyle{ g = g' }[/math] and [math]\displaystyle{ (h,h') }[/math] is an edge of [math]\displaystyle{ H }[/math].

The other name is Wreath product.