Adjacent forest graph

Adjacent forest graph — смежный граф лесов.

Let [math]\displaystyle{ \,G }[/math] be a connected graph. Given [math]\displaystyle{ 1 \leq \omega \leq |V(G)| - 1 }[/math], the adjacent forest graph of [math]\displaystyle{ \,G }[/math], denoted by [math]\displaystyle{ F_{\omega}^{a}(G) }[/math], is defined as a spanning subgraph of a forest graph [math]\displaystyle{ \,F_{\omega}(G) }[/math]; its two vertices are adjacent if and only if the only two edges in the symmetric difference of their corresponding forests are adjacent in [math]\displaystyle{ \,G }[/math].

See

• Forest graph.