Fair Restrained Domination in Graphs

Enriquez, Enrico L.

doi:10.14445/22315373/ijmtt-v66i1p530

Cited by 12 publications

(12 citation statements)

References 4 publications

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“…It's noteworthy that the set 𝑆 = 𝑉(𝐺) constitutes a restrained dominating set, and determining is 𝛾 𝑟 (𝐺), an NP-complete decision problem [19]. Several studies on restrained domination in graphs can be found in papers [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Outer-restrained Domination in the Lexicographic Product of Two Graphs

et al. 2024

IJFMR

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Let G be a connected simple graph. A set S⊆V(G) is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in (G)∖S . A set S of vertices of a graph G is an outer-restrained dominating set if every vertex not in S is adjacent to some vertex in S and V(G)∖S is a restrained set. The outer-restrained domination number of G, denoted by (γ_r ) ̃(G) is the minimum cardinality of an outer-restrained dominating set of G. An outer-restrained set of cardinality (γ_r ) ̃(G) will be called a (γ_r ) ̃(G) -set. This study is an extension of an existing research on outer-restrained domination in graphs. In this paper, we characterized the outer-restrained domination in graphs under the lexicographic product of two graphs.

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Section: Introductionmentioning

confidence: 99%

Outer-restrained Domination in the Lexicographic Product of Two Graphs

et al. 2024

IJFMR

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“…The domination number 𝛾(𝐺) of a graph 𝐺 is the smallest number of vertices in any minimum dominating set. Numerous types of dominating sets [4][5][6][7][8][9][10][11][12][13][14][15][16] have been discovered since the introduction of domination theory. One type of a dominating set is the inverse dominating set.…”

Section: Introductionmentioning

confidence: 99%

“…The dominating set 𝑆 ⊆ 𝑉(𝐺) ∖ 𝐷 is called an inverse dominating set of 𝐺 with respect to a minimum dominating set 𝐷. The concept of inverse domination in graphs was first introduced by Kulli [17], with further information in [18][19][20][21][22][23][24][25][26]. Another type is the disjoint dominating set, defined by Hedetniemi et al [27].…”

Section: Introductionmentioning

confidence: 99%

Disjoint Perfect Secure Domination in the Cartesian Product and Lexicographic Product of Graphs

et al. 2024

IJFMR

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Let G be a graph. A dominating set D⊆V(G) is called a secure dominating set of G if for each vertex u∈V(G)∖D, there exists a vertex v∈D such that uv∈ E(G) and the set (D∖{v})∪{u} is a dominating set of G. If every u∈V(G)∖D is adjacent to exactly one vertex in D, then D is a perfect secure dominating set of G. Let D be a minimum perfect secure dominating set of G. If S⊆V(G)∖D is a perfect secure dominating set of G, then S is called an inverse perfect secure dominating set of G with respect to D. A disjoint perfect secure dominating set of G is the set C=D∪S⊆V(G). Furthermore, the disjoint perfect secure domination number, denoted by γ_ps γ_ps (G), is the minimum cardinality of a disjoint perfect secure dominating set of G. A disjoint perfect secure dominating set of cardinality γ_ps γ_ps (G) is called γ_ps γ_ps-set. In this paper, we extended the study on the concept of disjoint perfect secure domination in graphs. Furthermore, we characterized the disjoint perfect secure domination in the Cartesian product and lexicographic product of two graphs.

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“…A dominating subset of is a fair dominating set of if all the vertices not in are dominated by the same number of vertices from that is for every two distinct vertices and from and a subset of is a -fair dominating set in if for every vertex , The minimum cardinality of a fair dominating set of denoted by is called the fair domination number of A fair dominating set of cardinality is called -set. A related paper on fair domination in graphs is found in [16,17]. Other variant of domination in a graph is the super dominating sets in graphs initiated by Lemanska et.al.…”

Section: Introductionmentioning

confidence: 99%