Algorithm complexity of neighborhood total domination and (ρ,γnt)-graphs
A neighborhood total dominating set, abbreviated for NTD-set D , is a vertex set of G such that D is a dominating set with an extra property: the subgraph induced by the open neighborhood of D has no isolated vertex. The neighborhood total domination number, denoted by γ n t ( G ) , is the minimum c...
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| Veröffentlicht in: | Journal of combinatorial optimization Jg. 35; H. 2; S. 424 - 435 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.02.2018
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1382-6905, 1573-2886 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A neighborhood total dominating set, abbreviated for NTD-set
D
, is a vertex set of
G
such that
D
is a dominating set with an extra property: the subgraph induced by the open neighborhood of
D
has no isolated vertex. The neighborhood total domination number, denoted by
γ
n
t
(
G
)
, is the minimum cardinality of a NTD-set in
G
. In this paper, we prove that NTD problem is NP-complete for bipartite graphs and split graphs. Then we give a linear-time algorithm to determine
γ
n
t
(
T
)
for a given tree
T
. Finally, we characterize a constructive property of
(
γ
n
t
,
2
γ
)
-trees and provide a constructive characterization for
(
ρ
,
γ
n
t
)
-graphs, where
γ
and
ρ
are domination number and packing number for the given graph, respectively. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1382-6905 1573-2886 |
| DOI: | 10.1007/s10878-017-0181-6 |