Strong product of graphs

Strong product of graphs --- сильное произведение графов.

For given graphs [math]\displaystyle{ G_{i} = (V_{i},E_{i}) }[/math], [math]\displaystyle{ i = 1, \ldots, n }[/math], the vertex set of the product graph [math]\displaystyle{ G = (V,E) }[/math] is the Cartesian product of the vertex sets of the factors [math]\displaystyle{ G_{i} }[/math], i.e. [math]\displaystyle{ V = \{(a_{1}, \ldots, a_{n})\} }[/math], where [math]\displaystyle{ a_{i} \in V_{i} }[/math]. Two vertices [math]\displaystyle{ \bar{a} = (a_{1}, \ldots, a_{n}) }[/math] and [math]\displaystyle{ \bar{b} = (b_{1}, \ldots, b_{n}) }[/math] are adjacent in [math]\displaystyle{ n }[/math]-fold strong product if and only if for each [math]\displaystyle{ i }[/math], [math]\displaystyle{ 1 \leq i \leq n }[/math], either [math]\displaystyle{ (a_{i},b_{i}) }[/math] is an edge in [math]\displaystyle{ G_{i} }[/math] or [math]\displaystyle{ a_{i} = b_{i} }[/math].