Bounds on the hop domination number of a tree

Ayyaswamy, S. K.; Krishnakumari, B.; Natarajan, C.; Venkatakrishnan, Y. B.

doi:10.1007/s12044-015-0251-6

Cited by 32 publications

(23 citation statements)

References 3 publications

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“…Recently, Natarajan and Ayyaswamy [10] introduced and studied the concept of hop domination in a graph. In another study, Ayyaswamy et al [1] investigated the same concept and gave bounds of the hop domination number of some graphs. Henning and Rad [7] also studied the concept and answered a question posed by Ayyaswamy and Natarajan in [10].…”

Section: Introductionmentioning

confidence: 99%

Global Hop Domination Numbers of Graphs

Salasalan

Canoy

2021

Eur. J. Pure Appl. Math.

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A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. It is a global hop dominating set of G if it is a hop dominatingset of both G and the complement of G. The minimum cardinality of a global hop dominatingset of G, denoted by γgh(G), is called the global hop domination number of G. In this paper, we study the concept of global hop domination in graphs resulting from some binary operations.

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Section: Introductionmentioning

confidence: 99%

Global Hop Domination Numbers of Graphs

Salasalan

Canoy

2021

Eur. J. Pure Appl. Math.

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“…The hop degree of a vertex v in a graph denoted by d h (v) is the number of vertices at distance= 2 from v. The hop graph H(G) of a graph G is the graph having same vertex set and two vertices u, v are adjacent in H(G) iff d G (u, v) = 2. Also, Ayyasamy et al [2] obtained some bounds on hop domination number for trees and characterized trees attaining those bounds. Natarajan et al [13] found characterization results for hop domination number equals other domination parameters like total domination number, connected domination number for several families of graphs.…”

Section: Introductionmentioning

confidence: 99%

On Hop Domination Number of Some Generalized Graph Structures

Shanmugavelan

Natarajan

2021

UMJ

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A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denoted by \(\gamma_{h}(G)\). In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.

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“…Recently, Natarajan and Ayyaswamy [6] introduced and studied the concept of hop domination in a graph. In another study, Ayyaswamy et al [2] investigated the same concept and gave bounds of the hop domination number of some graphs. Henning and Rad [5] also studied the concept and answered a question posed by Ayyaswamy and Natarajan in [6].…”

Section: Introductionmentioning

confidence: 99%

Hop Dominating Sets in Graphs Under Binary Operations

Canoy

Mollejon

Canoy³

2019

Eur. J. Pure Appl. Math.

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Let G be a (simple) connected graph with vertex and edge sets V (G) and E(G),respectively. A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. The minimum cardinality of a hop dominating set of G, denoted by γh(G), is called the hop domination number of G. In this paper we revisit the concept of hop domination, relate it with other domination concepts, and investigate it in graphs resulting from some binary operations.

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Bounds on the hop domination number of a tree

Cited by 32 publications

References 3 publications

Global Hop Domination Numbers of Graphs

Global Hop Domination Numbers of Graphs

On Hop Domination Number of Some Generalized Graph Structures

Hop Dominating Sets in Graphs Under Binary Operations

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