Weakly-connected dominating set: различия между версиями

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A ''' weakly-connected dominating set''', <math>{\mathcal W}</math>, of a graph <math>G</math> is
A ''' weakly-connected dominating set''', <math>{\mathcal W}</math>, of a graph <math>G</math> is
a domi\-nating set such that the subgraph consisting of <math>V(G)</math> and all
a dominating set such that the subgraph consisting of <math>V(G)</math> and all
edges incident with vertices in <math>{\mathcal W}</math> is connected. Define the
edges incident with vertices in <math>{\mathcal W}</math> is connected. Define the
minimum cardinality of all weakly-connected dominating sets of <math>G</math> as
minimum cardinality of all weakly-connected dominating sets of <math>G</math> as
the ''' weakly-connected domination number''' of <math>G</math> and denote this
the ''' weakly-connected domination number''' of <math>G</math> and denote this
by <math>\gamma_{w}(G)</math>.
by <math>\gamma_{w}(G)</math>.

Текущая версия от 14:35, 30 августа 2011

Weakly-connected dominating set --- слабо связное доминирующее множество.

A weakly-connected dominating set, [math]\displaystyle{ {\mathcal W} }[/math], of a graph [math]\displaystyle{ G }[/math] is a dominating set such that the subgraph consisting of [math]\displaystyle{ V(G) }[/math] and all edges incident with vertices in [math]\displaystyle{ {\mathcal W} }[/math] is connected. Define the minimum cardinality of all weakly-connected dominating sets of [math]\displaystyle{ G }[/math] as the weakly-connected domination number of [math]\displaystyle{ G }[/math] and denote this by [math]\displaystyle{ \gamma_{w}(G) }[/math].