Partial Domination in the Join, Corona, Lexicographic and Cartesian Products of Graphs

Macapodi, Roselainie Dimasindil; Isla, Rowena T.; Canoy, Sergio R.

doi:10.17654/dm020020277

Cited by 3 publications

(5 citation statements)

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“…The following concept is introduced in R. Macapodi et al [7] and is used to characterize partial dominating sets in the join of graphs.…”

Section: Proofmentioning

confidence: 99%

“…In 2019, R. Macapodi, R. Isla and S. Canoy [7] characterized the partial dominating sets in the join, corona, lexicographic and Cartesian products of graphs and determined the exact values or sharp bounds of the corresponding partial domination number of the said graphs. In the same year, R. Macapodi and R. Isla [10] published another paper where they characterized the total partial dominating sets in the join, corona, lexicographic product and Cartesian product of graphs.…”

Section: Introductionmentioning

confidence: 99%

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On Connected Partial Domination in Graphs

Cabulao

Isla²

2021

Eur. J. Pure Appl. Math.

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This paper introduces and investigates a variant of partial domination called the connected Î±-partial domination. For any graph G = (V (G), E(G)) and Î± âˆˆ (0, 1], a set S âŠ† V (G) is an Î±-partial dominating set in G if |N[S]| â‰¥ Î± |V (G)|. An Î±-partial dominating set S âŠ† V (G) is a connected Î±-partial dominating set in G if âŸ¨SâŸ©, the subgraph induced by S, is connected. The connected Î±-partial domination number of G, denoted by âˆ‚CÎ±(G), is the smallest cardinality of a connected Î±-partial dominating set in G. In this paper, we characterize the connected Î±-partial dominating sets in the join and lexicographic product of graphs for any Î± âˆˆ (0, 1] and determine the corresponding connected Î±-partial domination numbers of graphs resulting from the said binary operations. Moreover, we establish sharp bounds for the connected Î±-partial domination numbers of the corona and Cartesian product of graphs. Furthermore, we determine âˆ‚CÎ±(G) of some special graphs when Î± =1/2. Several realization problems are also generated in this paper.

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“…The following concept is introduced in R. Macapodi et al [7] and is used to characterize partial dominating sets in the join of graphs.…”

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Connected Partial Domination in Graphs

Cabulao

Isla²

2021

Eur. J. Pure Appl. Math.

Self Cite

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“…The following characterizations of partial dominating sets in the join, corona, lexicographic product and Cartesian product of graphs are found in Macapodi et al [3].…”

Section: Case 2: B = 2amentioning

confidence: 99%

“…Das [2] also studied different bounds on the partial domination number of a graph with respect to several parameters like its order, maximum degree, and domination number. Macapodi, Isla and Canoy [3] characterized the partial dominating sets in the join, corona, lexicographic product and Cartesian product of graphs and determined the exact values or sharp bounds of the corresponding partial domination number of these graphs. They also introduced and examined the concepts of total partial domination and (α, k)-partial domination, where α ∈ (0, 1] and k ∈ (−∞, 0].…”

Section: Introductionmentioning

confidence: 99%

Total Partial Domination in Graphs Under Some Binary Operations

Macapodi

Isla

2019

Eur. J. Pure Appl. Math.

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Let G = (V (G), E(G)) be a simple graph and let α ∈ (0, 1]. A set S ⊆ V (G) isan α-partial dominating set in G if |N[S]| ≥ α |V (G)|. The smallest cardinality of an α-partialdominating set in G is called the α-partial domination number of G, denoted by ∂α(G). An α-partial dominating set S ⊆ V (G) is a total α-partial dominating set in G if every vertex in S isadjacent to some vertex in S. The total α-partial domination number of G, denoted by ∂T α(G), isthe smallest cardinality of a total α-partial dominating set in G. In this paper, we characterize thetotal partial dominating sets in the join, corona, lexicographic and Cartesian products of graphsand determine the exact values or sharp bounds of the corresponding total partial dominationnumber of these graphs.

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“…The theory of domination is one of the profusely researched areas in graph theory. Recently a new domination parameter called partial domination number was introduced simultaneously in [3], [4] and [6], and studied in [12,13,14,15]. We extend the concept of partial domination to independent domination in graphs.…”

Section: Introductionmentioning

confidence: 99%

Independent partial domination

Nithya

Kureethara

2021

Cubo

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For p ∈ (0, 1], a set S ⊆ V is said to p-dominate or partially dominate a graphThe minimum cardinality among all p-dominating sets is called the p-domination number and it is denoted by γp(G). Analogously, the independent partial domination (ip(G)) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number βp(G) are defined and some of their properties are presented. Finally, the partial domination chain is established as γpRESUMEN Para p ∈ (0, 1], un conjunto S ⊆ V se dice que pdomina o parcialmente domina un grafo G = (V, E) si |N [S]| |V |

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Partial Domination in the Join, Corona, Lexicographic and Cartesian Products of Graphs

Cited by 3 publications

References 0 publications

On Connected Partial Domination in Graphs

On Connected Partial Domination in Graphs

Total Partial Domination in Graphs Under Some Binary Operations

Independent partial domination

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