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On domination in signed graphs Cover

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.

Language: English
Page range: 1 - 9
Submitted on: Feb 20, 2023
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Published on: Aug 8, 2023
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 James Joseph, Mayamma Joseph, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.