International Journal of Nonlinear Analysis and Applications
Stability and some results of triple effect domination
Document Type : Research Paper
Authors
Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
Abstract
Let $G=(V, E)$ be a graph without isolated vertices. A subset $D \subseteq V$ is triple effect dominating set, if every vertex in $D$ dominates exactly three vertices of $V-D$. The triple effect domination number $\gamma_{t e}(G)$ is the minimum cardinality over all triple effect dominating sets in $G$. In this paper, the triple effect domination number $\gamma_{t e}(G)$ is studied to be changing or not after adding or deleting edge or deleting vertex. Some conditions are putted on the graph to be affected or not with several results and examples. Then, the triple effect domination and its inverse is applied on several graphs obtained from complement, join and corona operations.
Keywords
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Volume 14, Issue 4
April 2023Pages 349-358
- Receive Date: 16 February 2022
- Revise Date: 20 March 2022
- Accept Date: 27 April 2022