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Secure convex domination in a graph
TLDR
We show that given positive integers k and n such that n ≥ 4 and 1 ≤ k ≤ n, there exists a connected graph G with |V (G)| = n and γscon(G) = k. Expand
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On a variant of convex domination in a graph
Abstract A dominating set S which is also convex is called a convex dominating set of G. A convex dominating set S of V (G) is a restrained convex dominating set of G if for each u ∈ V (G) \ S, thereExpand
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Outer-convex domination in graphs
TLDR
A set S of vertices of a graph G is an outer-convex dominating set if every vertex not in S is adjacent to some vertex in S and V (G) is a convex set. Expand
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Inverse Clique Domination in Graphs
Let G be a connected simple graph. A nonempty subset S of the vertex set V (G) is a clique in G if the graph induced by S is complete. A clique S in G is a clique dominating set if it is a dominatingExpand
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Disjoint Secure Domination in the Join of Graphs
Let G = (V(G),E(G)) be a simple connected graph. A dominating set S in G is called a secure dominating set in G if for every u ∈ V (G) \ S, there exists v ∈ S ∩ NG(u) such that (S \ {v}) ∪ {u} is aExpand
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z-DOMINATION IN GRAPHS
Let be a connected simple graph. A subset of a vertex setis a dominating set of if for every vertex there exists a vertexsuch thatis an edge of Let  be a minimum dominating set in The dominating setExpand
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ON RESTRAINED CLIQUE DOMINATION IN GRAPHS
Abstract:  Let  be a connected simple graph. A nonempty subset  of the vertex set  is a clique in  if the graph  induced by  is complete. A clique  in  is a clique dominating set if it is aExpand
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Outer-Clique Domination in Graphs
Let  be a simple graph. A set of vertices of a graph is an outer-clique dominating set if every vertex not in  is adjacent to some vertex inand the subgraph induced by is clique. In this paper, weExpand
Super Fair Dominating Set in the Cartesian Product of Graphs
In this paper, we characterize the super fair dominating set in the Cartesian product of two graphs and give some important results.
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