Generalized connected domination in graphs
As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c k (G) of such a smallest set we relate to γ c (G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c k (T) in terms of...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2006-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/460 |
| id |
doaj-08b036f1e4f744c3a2acbe223dceab47 |
|---|---|
| record_format |
Article |
| spelling |
doaj-08b036f1e4f744c3a2acbe223dceab472020-11-24T21:01:24ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502006-01-0181Generalized connected domination in graphsM. KouiderP.D. VestergaardAs a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c k (G) of such a smallest set we relate to γ c (G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c k (T) in terms of minimum valency and diameter. For trees the inequality γ c k (T)≤ n-k-1 is known to hold, we determine the class of trees, for which equality holds. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/460 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Kouider P.D. Vestergaard |
| spellingShingle |
M. Kouider P.D. Vestergaard Generalized connected domination in graphs Discrete Mathematics & Theoretical Computer Science |
| author_facet |
M. Kouider P.D. Vestergaard |
| author_sort |
M. Kouider |
| title |
Generalized connected domination in graphs |
| title_short |
Generalized connected domination in graphs |
| title_full |
Generalized connected domination in graphs |
| title_fullStr |
Generalized connected domination in graphs |
| title_full_unstemmed |
Generalized connected domination in graphs |
| title_sort |
generalized connected domination in graphs |
| publisher |
Discrete Mathematics & Theoretical Computer Science |
| series |
Discrete Mathematics & Theoretical Computer Science |
| issn |
1462-7264 1365-8050 |
| publishDate |
2006-01-01 |
| description |
As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c k (G) of such a smallest set we relate to γ c (G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c k (T) in terms of minimum valency and diameter. For trees the inequality γ c k (T)≤ n-k-1 is known to hold, we determine the class of trees, for which equality holds. |
| url |
http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/460 |
| work_keys_str_mv |
AT mkouider generalizedconnecteddominationingraphs AT pdvestergaard generalizedconnecteddominationingraphs |
| _version_ |
1716778098201985024 |