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DOMINATION NUMBERS OF GRID GRAPHS
"... In this paper we deal with the domination numbers of the complete grid graphs ..."
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In this paper we deal with the domination numbers of the complete grid graphs
THE DOMINATION NUMBER OF A TOURNAMENT
, 2001
"... Abstract. We find bounds for the domination number of a tournament and investigate the sharpness of these bounds. We also find the domination number of a random tournament. ..."
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Abstract. We find bounds for the domination number of a tournament and investigate the sharpness of these bounds. We also find the domination number of a random tournament.
Game domination number
"... The game domination number of a (simple, undirected) graph is defined by the following game. Two players, A and D, orient the edges of the graph alternately until all edges are oriented. Player D starts the game, and his goal is to decrease the domination number of the resulting digraph, while A is ..."
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The game domination number of a (simple, undirected) graph is defined by the following game. Two players, A and D, orient the edges of the graph alternately until all edges are oriented. Player D starts the game, and his goal is to decrease the domination number of the resulting digraph, while A
LOWER BOUNDS FOR THE DOMINATION NUMBER
"... In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least twothirds of the radius of the graph, three times the domination number is at least two more than the number of cutvertices in the graph ..."
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In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least twothirds of the radius of the graph, three times the domination number is at least two more than the number of cut
On the domination number of some graphs
, 2008
"... Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of graph G, if every vertex in V − S is adjacent to at least one vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. It is well known that if e ∈ E(G), then γ(G − e)−1 ≤ γ(G) ≤ γ(G − e). In thi ..."
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Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of graph G, if every vertex in V − S is adjacent to at least one vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. It is well known that if e ∈ E(G), then γ(G − e)−1 ≤ γ(G) ≤ γ(G − e
ON DOMINATION NUMBERS OF GRAPH BUNDLES
, 2005
"... Let γ(G) be the domination number of a graph G. It is shown that for any k ≥ 0 there exists a Cartesian graph bundle B✷ϕF such that γ(B✷ϕF)=γ(B)γ(F)−2k. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement simila ..."
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Let γ(G) be the domination number of a graph G. It is shown that for any k ≥ 0 there exists a Cartesian graph bundle B✷ϕF such that γ(B✷ϕF)=γ(B)γ(F)−2k. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement
Bounds on the weak domination number
 Australas. J. Combin
, 1998
"... Let G = (V, E) a graph. A set D ~ V is a weak dominating set of G if for every vertex y E V D there is a vertex xED with xy E E and d ( x, G)::; d(y, G). The weak domination number rw (G) is defined as the minimum cardinality of a weak dominating set and was introduced by Sampathkumar and Pushpa La ..."
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Cited by 3 (1 self)
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Let G = (V, E) a graph. A set D ~ V is a weak dominating set of G if for every vertex y E V D there is a vertex xED with xy E E and d ( x, G)::; d(y, G). The weak domination number rw (G) is defined as the minimum cardinality of a weak dominating set and was introduced by Sampathkumar and Pushpa
Signed domination numbers of graphs
, 2004
"... Let G be a finite connected simple graph with vertex set V (G) and edge set E(G). A function f: V (G) → {−1, 1} is a signed dominating function if for every vertex v ∈ V (G), the closed neighborhood of v contains more vertices with function values 1 than with −1. The signed domination number γs(G) ..."
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Let G be a finite connected simple graph with vertex set V (G) and edge set E(G). A function f: V (G) → {−1, 1} is a signed dominating function if for every vertex v ∈ V (G), the closed neighborhood of v contains more vertices with function values 1 than with −1. The signed domination number γs
The domination number of exchanged hypercubes
, 2013
"... Exchanged hypercubes [Loh et al., IEEE Transactions on Parallel and Distributed Systems 16 (2005) 866–874] are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. Lower and upper bounds on the domination number of exchanged hy ..."
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Exchanged hypercubes [Loh et al., IEEE Transactions on Parallel and Distributed Systems 16 (2005) 866–874] are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. Lower and upper bounds on the domination number of exchanged
Distance domination numbers of . . .
, 2006
"... The distance ℓdomination number γℓ(G) of a strongly connected digraph G is the minimum number γ for which there is a set D ⊂ V (G) with cardinality γ such that any vertex v / ∈ D can be reached within distance ℓ from some vertex in D. In this paper, we establish a lower bound and an upper bound for ..."
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The distance ℓdomination number γℓ(G) of a strongly connected digraph G is the minimum number γ for which there is a set D ⊂ V (G) with cardinality γ such that any vertex v / ∈ D can be reached within distance ℓ from some vertex in D. In this paper, we establish a lower bound and an upper bound
Results 1  10
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16,104