<abstract xmlns="http://www.w3.org/1999/xhtml"> Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.</abstract>

Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.

Hop Domination in Graphs-II

Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur - 613 401, Tamilnadu,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Hop Domination in Graphs-II"}

Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum...

Hop Domination in Graphs-II

Published Online: Apr 22, 2017

Page range: 187 - 199

Received: Nov 01, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0036

Keywords
Hop domination number, total domination number, connected domination number

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Hop Domination in Graphs-II

Published Online: Apr 22, 2017

Page range: 187 - 199

Received: Nov 01, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0036

KeywordsHop domination number, total domination number, connected domination number

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hop domination number, total domination number, connected domination number