Abstract

Let G = (V, E) be a graph and let S⊆V. The set S is a co-secure dominating set (CSDS) of a graph G if S is a dominating set, and for each u ∈S there exists a vertex v ∈ V \ S such that uv ∈E(G) and (S \ {u})∪ {v} is a dominating set. The minimum cardinality of a co-secure dominating set in G is the co-secure domination number 𝛾𝑐𝑠 (G). We determine the co-secure domination number of some families of standard graphs and obtain sharp bounds. A set S ⊆V is a secure dominating set of a graph G = (V, E),if for each u ∈V \ S there exists a vertex v ∈ S such that uv ∈ E and (S \ {v}) ∪{u} is a dominating set. The minimum cardinality of a secure dominating set in G is the secure domination number 𝛾𝑠 (G). We present few bounds on these parameter band certain graphs for which equality of both parameter holds

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References

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