Adjacent forest graph: различия между версиями

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'''Adjacent forest graph''' --- смежный граф лесов.  
'''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 graphсмежный 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