On weakly connected domination in graphs
JE Dunbar, JW Grossman, JH Hattingh… - Discrete …, 1997 - Elsevier
Discrete Mathematics, 1997•Elsevier
A weakly connected dominating set for a connected graph is a dominating set D of vertices
of the graph such that the edges not incident to any vertex in D do not separate the graph.
This paper considers the weakly connected domination number, γw, and related domination
parameters. It is shown that the problem of computing γw is NP-hard in general but linear for
trees. In addition, several sharp upper and lower bounds for γw are obtained.
of the graph such that the edges not incident to any vertex in D do not separate the graph.
This paper considers the weakly connected domination number, γw, and related domination
parameters. It is shown that the problem of computing γw is NP-hard in general but linear for
trees. In addition, several sharp upper and lower bounds for γw are obtained.
A weakly connected dominating set for a connected graph is a dominating set D of vertices of the graph such that the edges not incident to any vertex in D do not separate the graph. This paper considers the weakly connected domination number, γw, and related domination parameters. It is shown that the problem of computing γw is NP-hard in general but linear for trees. In addition, several sharp upper and lower bounds for γw are obtained.
Elsevier
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