Adjacent forest graph

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Adjacent forest graphсмежный граф лесов.

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