Badouisth Badouier - Academia.edu (original) (raw)
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Let G be a connected nontrivial graph. A nonempty subset S of V (G) is a 1movable restrained domi... more Let G be a connected nontrivial graph. A nonempty subset S of V (G) is a 1movable restrained dominating set of G if S is a restrained dominating set of G and for every v ∈ S, S \ {v} is a restrained dominating set of G or there exists u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a restrained dominating set of G. The 1-movable restrained domination number of a graph G, denoted by γ 1 mr(G), is the cardinality of the smallest 1-movable restrained dominating set of G. A 1-movable restrained dominating set of G with cardinality equal to γ 1 mr(G) is called γ 1 mr -set of G. This paper presents some properties of 1-movable restrained dominating set and investigates the 1-movable restrained dominating sets in the join of two graphs. Moreover, the bounds or exact values of the 1-movable restrained domination number are determined. AMS subject classification: 05C69.
Let G be a connected nontrivial graph. A nonempty subset S of V (G) is a 1movable restrained domi... more Let G be a connected nontrivial graph. A nonempty subset S of V (G) is a 1movable restrained dominating set of G if S is a restrained dominating set of G and for every v ∈ S, S \ {v} is a restrained dominating set of G or there exists u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a restrained dominating set of G. The 1-movable restrained domination number of a graph G, denoted by γ 1 mr(G), is the cardinality of the smallest 1-movable restrained dominating set of G. A 1-movable restrained dominating set of G with cardinality equal to γ 1 mr(G) is called γ 1 mr -set of G. This paper presents some properties of 1-movable restrained dominating set and investigates the 1-movable restrained dominating sets in the join of two graphs. Moreover, the bounds or exact values of the 1-movable restrained domination number are determined. AMS subject classification: 05C69.