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

In an isolate-free graph 𝒵 = (V𝒵, E𝒵), a set <italic>C</italic> of vertices is termed as a connected certified dominating set of 𝒵 if, |N𝒵(<italic>u</italic>) ∩ (V𝒵\<italic>C</italic>)| = 0 or |N𝒵(<italic>u</italic>) ∩ (V𝒵\<italic>C</italic>)| ≥ 2 ∀u ∈<italic>C</italic>, and the subgraph 𝒵[<italic>C</italic>] induced by <italic>C</italic> is connected. The cardinality of the minimal connected certified dominating set of graph 𝒵 is called the connected certified domination number of 𝒵 denoted by γcerc (<italic>Z</italic>). In graph 𝒵, if the deletion of any arbitrary edge changes the connected certified domination number, then we call it a connected certified domination edge critical. If the deletion of any random edge does not a ect the connected certified domination number, then we refer to it as a connected certified domination edge stable graph. In this paper, we investigate those graphs which are connected certified domination edge critical and stable upon edge removal. We then study some properties of connected certified domination edge critical and stable graphs.
</abstract>

In an isolate-free graph 𝒵 = (V𝒵, E𝒵), a set C of vertices is termed as a connected certified dominating set of 𝒵 if, |N𝒵(u) ∩ (V𝒵\C)| = 0 or |N𝒵(u) ∩ (V𝒵\C)| ≥ 2 ∀u ∈C, and the subgraph 𝒵[C] induced by C is connected. The cardinality of the minimal connected certified dominating set of graph 𝒵 is called the connected certified domination number of 𝒵 denoted by γcerc (Z). In graph 𝒵, if the deletion of any arbitrary edge changes the connected certified domination number, then we call it a connected certified domination edge critical. If the deletion of any random edge does not a ect the connected certified domination number, then we refer to it as a connected certified domination edge stable graph. In this paper, we investigate those graphs which are connected certified domination edge critical and stable upon edge removal. We then study some properties of connected certified domination edge critical and stable graphs.

Connected certified domination edge critical and stable graphs

Acta Universitatis Sapientiae, Informatica

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

{"article-title":"Connected certified domination edge critical and stable graphs"}

In an isolate-free graph 𝒵 = (V𝒵, E𝒵), a set C of vertices is termed as a connected certified dominating set of 𝒵 if, |N𝒵(u) ∩ (V𝒵\C)| = 0 or |N𝒵(u) ∩...

Connected certified domination edge critical and stable graphs

Publié en ligne: 08 août 2023

Pages: 25 - 37

Reçu: 30 janv. 2023

DOI: https://doi.org/10.2478/ausi-2023-0003

Mots clés
connected certified domination, connected certified domination edge critical, connected certified domination edge stable

© 2023 Azham Ilyass Lone et al., published by Sciendo

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

Connected certified domination edge critical and stable graphs

Publié en ligne: 08 août 2023

Pages: 25 - 37

Reçu: 30 janv. 2023

DOI: https://doi.org/10.2478/ausi-2023-0003

Mots clésconnected certified domination, connected certified domination edge critical, connected certified domination edge stable

© 2023 Azham Ilyass Lone et al., published by Sciendo

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

Mots clés
connected certified domination, connected certified domination edge critical, connected certified domination edge stable