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Keywords
(2)
Dominating Set
Domination Number
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(2)
R Domination in Graphs
Domination in Graphs: Advanced Topics
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Strong weak domination and domination balance in a graph
Strong weak domination and domination balance in a graph,10.1016/0012365X(95)00231K,Discrete Mathematics,E. Sampathkumar,L. Pushpa Latha
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Strong weak domination and domination balance in a graph
(
Citations: 6
)
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E. Sampathkumar
,
L. Pushpa Latha
Let G = (V, E) be a graph and u, v ~ V. Then, u strongly dominates v and v weakly dominates u if (i) uv ~ E and (ii) deg u >/deg v. A set D c V is a strongdominating set (sdset) of G if every vertex in V  D is strongly dominated by at least one vertex in D. Similarly, a weakdominating set (wdset) is defined. The strong (weak)
domination number
7s (7w) of G is the minimum cardinality of an sdset (wdset). Besides investigating some relationship of ?s and ?w with other known parameters of G, some bounds are obtained. A graph G is domination balanced if there exists an sdset D1 and a wdset/)2 such that D1 c~D2 = 0. A study of domination balanced graphs is initiated.
Journal:
Discrete Mathematics  DM
, vol. 161, no. 13, pp. 235242, 1996
DOI:
10.1016/0012365X(95)00231K
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Citation Context
(3)
...i) the induced subgraphhSi is connected, then S is a connected dominating set (Sampathkumar and Walikar [
14
]);...
...iii) for all u2 V S, there exists a vertex v2 S such that uv2 E and deg(v) deg(u), then S is called a strong dominating set, and S is a weak dominating set if, for all u 2 V S, there exists a vertex v 2 S such that uv 2 E and deg(v) deg(u) (Pushpa Latha and Sampathkumar [
14
])...
S. Balasubramanian
,
et al.
Gallai Theorems Involving Domination Parameters
...The strong domination and independent strong domination numbers were studied in [6, 9, 13, 14,
16
]...
...Corollary 1 (Sampathkumar and Pushpa Latha [
16
]) Any K1;3free graph is strong domination perfect...
...The weak domination number ∞W(G) is the minimum cardinality of a weak dominating set of G, and the independent weak domination number iW(G) is the minimum cardinality of an independent weak dominating set of G. Other results on these parameters can be found in [7, 8, 9, 15,
16
]...
...It was proved in [
16
] that any K1;3graph is weak domination perfect...
Dieter Rautenbach
,
et al.
Perfect graphs of strong domination and independent strong domination
...The strong domination and independent strong domination numbers were studied in [6,9,13,14,
16
]...
...Corollary 1 (Sampathkumar and Pushpa Latha [
16
])...
...It was proved in [
16
] that any K1;3graph is weak domination perfect...
D. Rautenbach
,
et al.
Perfect graphs of strong domination and independent strong domination
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Journal:
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Journal:
Discrete Mathematics  DM
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Citations
(6)
On strong (weak) independent sets and vertex coverings of a graph
S. S. Kamath
,
R. S. Bhat
Journal:
Discrete Mathematics  DM
, vol. 307, no. 910, pp. 11361145, 2007
Weak edgedegree domination in hypergraphs
Belmannu Devadas Acharya
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Purnima Gupta
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(
Citations: 4
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Journal:
Discrete Mathematics  DM
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(
Citations: 2
)
Dieter Rautenbach
Journal:
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