Sum of graphs

Sum of graphs --- сумма графов.

The sum [math]\displaystyle{ G_{1} + G_{2} }[/math] of graphs [math]\displaystyle{ G_{1} }[/math] and [math]\displaystyle{ G_{2} }[/math] is the graph with the vertex set [math]\displaystyle{ V(G_{1}) \times V(G_{2}) }[/math] in which two vertices [math]\displaystyle{ (u_{1},u_{2}) }[/math] and [math]\displaystyle{ (v_{1},v_{2}) }[/math] are adjacent if and only if [math]\displaystyle{ u_{1} = v_{1} }[/math] and [math]\displaystyle{ (u_{2},v_{2}) \in E_{2} }[/math] or [math]\displaystyle{ u_{2} = v_{2} }[/math] and [math]\displaystyle{ (u_{1},v_{1}) \in E_{1} }[/math].

See also

• Product of graphs.