<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V \ D] and within V \ D is balanced. The set D having least cardinality is called minimum restrained dominating set and its cardinality is the restrained domination number of Σ denoted by γ<sub>r</sub>(Σ). The ability to communicate rapidly within the network is an important application of domination in social networks. The main aim of this paper is to initiate a study on restrained domination in the realm of different classes of signed graphs.</p></abstract>

A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V \ D] and within V \ D is balanced. The set D having least cardinality is called minimum restrained dominating set and its cardinality is the restrained domination number of Σ denoted by γr(Σ). The ability to communicate rapidly within the network is an important application of domination in social networks. The main aim of this paper is to initiate a study on restrained domination in the realm of different classes of signed graphs.

Restrained domination in signed graphs

Acta Universitatis Sapientiae, Mathematica

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

{"article-title":"Restrained domination in signed graphs"}

A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even...

Restrained domination in signed graphs

Published Online: Jul 16, 2020

Page range: 155 - 163

Received: Nov 14, 2019

DOI: https://doi.org/10.2478/ausm-2020-0010

Keywords
signed graphs, dominating set, restrained dominating set, restrained domination number

© 2020 Anisha Jean Mathias et al., published by Sciendo

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

Restrained domination in signed graphs

Published Online: Jul 16, 2020

Page range: 155 - 163

Received: Nov 14, 2019

DOI: https://doi.org/10.2478/ausm-2020-0010

Keywordssigned graphs, dominating set, restrained dominating set, restrained domination number

© 2020 Anisha Jean Mathias et al., published by Sciendo

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

Keywords
signed graphs, dominating set, restrained dominating set, restrained domination number