Connected to relation: различия между версиями

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'''Connected to relation''' --- отношение связности ''к'', (достижимость) в гиперграфе.  
'''Connected to relation''' — ''[[отношение связности ''к'']], [[(достижимость) в гиперграфе]].''


The relation '''connected to''', which is denoted by the symbol
The relation '''connected to''', which is denoted by the symbol
<math>\succ</math>, is defined for a given subset <math>R</math> of nodes and a node <math>y</math>;
<math>\succ</math>, is defined for a given subset <math>\,R</math> of nodes and a [[node]] <math>\,y</math>;
we say that <math>R</math> is '''connected to''' <math>y</math> and write <math>R \succ y</math> if and only if a ''directed hyperpath'' exsists in a hypergraph from <math>R</math>
we say that <math>\,R</math> is '''connected to''' <math>\,y</math> and write <math>R \succ y</math> if and only if a ''[[directed hyperpath]]'' exsists in a [[hypergraph]] from <math>\,R</math>
to the node <math>y</math>.
to the node <math>\,y</math>.


It is easy to check that the relation <math>\succ</math> satisfies the following set of
It is easy to check that the relation <math>\succ</math> satisfies the following set of
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(3) <math>R \succ y, \; \forall y \in Y,\mbox{ and }Y \succ z \Rightarrow
(3) <math>R \succ y, \; \forall y \in Y,\mbox{ and }Y \succ z \Rightarrow
R \succ z</math> (transitivity).
R \succ z</math> (transitivity).
==Литература==
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия от 10:48, 24 октября 2018

Connected to relationотношение связности ''к'', (достижимость) в гиперграфе.

The relation connected to, which is denoted by the symbol [math]\displaystyle{ \succ }[/math], is defined for a given subset [math]\displaystyle{ \,R }[/math] of nodes and a node [math]\displaystyle{ \,y }[/math]; we say that [math]\displaystyle{ \,R }[/math] is connected to [math]\displaystyle{ \,y }[/math] and write [math]\displaystyle{ R \succ y }[/math] if and only if a directed hyperpath exsists in a hypergraph from [math]\displaystyle{ \,R }[/math] to the node [math]\displaystyle{ \,y }[/math].

It is easy to check that the relation [math]\displaystyle{ \succ }[/math] satisfies the following set of connectivity axioms:

(1) [math]\displaystyle{ y \in R \subseteq V \Rightarrow R \succ y }[/math] (reflexivity);

(2) [math]\displaystyle{ R \succ y\mbox{ and } Z \subseteq V \Rightarrow (R \cup Z) \succ y }[/math] (augmentation);

(3) [math]\displaystyle{ R \succ y, \; \forall y \in Y,\mbox{ and }Y \succ z \Rightarrow R \succ z }[/math] (transitivity).

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.