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On weakly connected domination in graphs
TLDR
A dominating set D is a weakly connected dominating set of a connected graph G if (V,E@?(DxV)) is connected. Expand
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The algorithmic complexity of signed domination in graphs
TLDR
A two-valued function f defined on the vertices of a graph G (V, E), I : V -+ {-I, I}, is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. Expand
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Majority domination in graphs
TLDR
A two-valued function f defined on the vertices of a graph G = (V, E) is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. Expand
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Star-path bipartite Ramsey numbers,
TLDR
In this note, we establish the exact value of the bipartite Ramsey number b ( P m , K l , n ) for all integers m , n ⩾ 2, where P m denotes a path on m vertices. Expand
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Restrained domination in graphs
TLDR
A restrained dominating set is a set S ⊆ V where every vertex in V − S is adjacent to a vertex in S as well as another vertex inV . Expand
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Restrained domination in trees
TLDR
We show that if T is a tree of order n , then γ r (T)⩾⌈(n+2)/3⌉ is the smallest cardinality of a restrained dominating set of G . Expand
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PRODUCTS OF CIRCULANT GRAPHS
ABSTRACT Graph products of circulants are studied. It is shown that if G and H are circulants and gcd(v(G), v(H)) = 1, then every B-product of G and H is again a circulant. We prove that if m ≠ 2,Expand
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Total restrained domination in unicyclic graphs 1
Let G = (V, E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V −S is adjacent to a vertex in V −S. The totalExpand
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The ratio of the distance irredundance and domination numbers of a graph
Let n ≥ 1 be an integer and let G be a graph. A set D of vertices in G is defined to be an n-dominating set of G if every vertex of G is within distance n from some vertex of D. The minimumExpand
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Using maximality and minimality conditions to construct inequality chains
TLDR
We define a simple mechanism which explains why this inequality chain exists and how it is possible to define many similar chains of potentially arbitrary length. Expand
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