<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article the concept of domination in signed graphs is examined from an alternate perspective and a new definition of the same is introduced. A vertex subset D of a signed graph S is a dominating set, if for each vertex v not in D there exists a vertex u ∈ D such that the sign of the edge uv is positive. The domination number γ (S) of S is the minimum cardinality among all the dominating sets of S. We obtain certain bounds of γ (S) and present a necessary and su cient condition for a dominating set to be a minimal dominating set. Further, we characterise the signed graphs having small and large values for domination number.</p>
</abstract>

In this article the concept of domination in signed graphs is examined from an alternate perspective and a new definition of the same is introduced. A vertex subset D of a signed graph S is a dominating set, if for each vertex v not in D there exists a vertex u ∈ D such that the sign of the edge uv is positive. The domination number γ (S) of S is the minimum cardinality among all the dominating sets of S. We obtain certain bounds of γ (S) and present a necessary and su cient condition for a dominating set to be a minimal dominating set. Further, we characterise the signed graphs having small and large values for domination number.

On domination in signed graphs

Acta Universitatis Sapientiae, Informatica

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

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

In this article the concept of domination in signed graphs is examined from an alternate perspective and a new definition of the same is introduced. A vertex...

On domination in signed graphs

Data publikacji: 08 sie 2023

Zakres stron: 1 - 9

Otrzymano: 20 lut 2023

DOI: https://doi.org/10.2478/ausi-2023-0001

Słowa kluczowe
signed graphs, dominating set, domination number, minimal dominating set

© 2023 James Joseph et al., published by Sciendo

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

On domination in signed graphs

Data publikacji: 08 sie 2023

Zakres stron: 1 - 9

Otrzymano: 20 lut 2023

DOI: https://doi.org/10.2478/ausi-2023-0001

Słowa kluczowesigned graphs, dominating set, domination number, minimal dominating set

© 2023 James Joseph et al., published by Sciendo

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

Słowa kluczowe
signed graphs, dominating set, domination number, minimal dominating set