Dierentiating-Dominating sets in graphs Under binary operations

Canoy, Sergio R.osales; Malacas, Gina A.

doi:10.5556/j.tkjm.46.2015.1553

Cited by 8 publications

(8 citation statements)

References 3 publications

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“…In fact, some real-life problems (including protection strategies and facility location) that can be modeled by the concept of domination can be slighty modified for the concept of hop domination. Domination, hop domination, and some of their variations are also studied in [1], [2], [9], [10], [11], [12], [13], and [16].…”

Section: Introductionmentioning

confidence: 99%

Grundy Hop Domination in Graphs

Hassan

Canoy

2022

Eur. J. Pure Appl. Math.

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Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. Let S = (v1, v2, · · · , vk) be a sequence of distinct vertices of G and let Sˆ = {v1, v2, . . . , vk}. Then S is a legal closed hop neighborhood sequence of G if N2 G[vi]\∪i−1j=1N 2 G[vj ] ̸= ∅ for each i ∈ {2, · · · , k}. If, in addition, Sˆ is a hop dominating set of G, then S is called a Grundy hop dominating sequence.The maximum length of a Grundy hop dominating sequence in a graph G, denoted by γ hgr(G), is called the Grundy hop domination number of G. In this paper, we determine some (extreme) values for the Grundy hop domination number. It is pointed out that the Grundy hop domination number is at least equal to the hop domination. Bounds for the Grundy hop domination numbersof some graphs resulting from some binary operations of two graphs are also obtained.

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Section: Introductionmentioning

confidence: 99%

Grundy Hop Domination in Graphs

Hassan

Canoy

2022

Eur. J. Pure Appl. Math.

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“…fire, burglar) can be singled out when a problem (presence of an intruder or fire) at a facility or system arises. The papers in [1], [2], [3], [4], and [5] also dealt with the concept of locating-domination and some of its related concepts.…”

Section: Introductionmentioning

confidence: 99%

Stable Locating-Dominating Sets in Graphs

Ahmad

Malacas

Canoy

2021

Eur. J. Pure Appl. Math.

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A set S âŠ† V(G) of a (simple) undirected graph G is a locating-dominating set of G if for each v âˆˆ V(G) \ S, there exists w âˆˆ S such tha vw âˆˆ E(G) and NG(x) âˆ© S= NG(y)âˆ©S for any distinct vertices x and y in V(G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v âˆˆ S. The minimum cardinality of a stable locating-dominating set of G, denoted by Î³sl(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for some graphs. Further, we introduce other related concepts and use them to characterize the stable locating-dominating sets in some graphs.

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“…The concepts of differentiating sets, differentiating-dominating sets and the associated parameters are studied in [2] and [4]. On the other hand, restrained domination in graphs is defined and studied in [6] and [7].…”

Section: Introductionmentioning

confidence: 99%

“…Lemma 3.12 [2] Let G be a point distinguishing graph of order n ≥ 3 such that dn(G) < γ D (G). Then 1 + dn(G) = γ D (G).…”

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confidence: 99%