Adjacent forest graph: различия между версиями
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Glk (обсуждение | вклад) (Создана новая страница размером '''Adjacent forest graph''' --- смежный граф лесов. Let <math>G</math> be a connected graph. Given <math>1 \leq \omega \...) |
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'''Adjacent forest graph''' | '''Adjacent forest graph''' — ''[[смежный граф лесов]].'' | ||
Let <math>G</math> be a connected graph. Given <math>1 \leq \omega \leq |V(G)| - 1</math>, | Let <math>\,G</math> be a [[connected graph]]. Given <math>1 \leq \omega \leq |V(G)| - 1</math>, | ||
the '''adjacent forest graph''' of <math>G</math>, denoted by | the '''adjacent forest graph''' of <math>\,G</math>, denoted by | ||
<math>F_{\omega}^{a}(G)</math>, is defined as a spanning subgraph of a ''forest graph'' <math>F_{\omega}(G)</math>; its two vertices are adjacent if and only if | <math>F_{\omega}^{a}(G)</math>, is defined as a [[spanning subgraph]] of a ''[[forest graph]]'' <math>\,F_{\omega}(G)</math>; its two [[vertex|vertices]] are adjacent if and only if | ||
the only two edges in the symmetric difference of their corresponding | the only two [[edge|edges]] in the symmetric difference of their corresponding | ||
forests are adjacent in <math>G</math>. | [[forest|forests]] are adjacent in <math>\,G</math>. | ||
==See== | ==See== | ||
*'' Forest graph''. | * ''[[Forest graph]]''. | ||
Текущая версия от 13:26, 17 ноября 2011
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].