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Semi Square Stable Graphs and Efficient Dominating Sets
- Source :
- Transactions on Combinatorics, Vol 12, Iss 2, Pp 107-113 (2023)
- Publication Year :
- 2023
- Publisher :
- University of Isfahan, 2023.
-
Abstract
- A graph $G$ is called semi square stable if $\alpha (G^{2})=i(G)$ where $%\alpha (G^{2})$ is the independence number of $G^{2}$ and $i(G)$ is the independent dominating number of $G$. A subset $S$ of the vertex set of a graph $G$ is an efficient dominating set if $S$ is an independent set and every vertex of $G$ is either in $S$ or adjacent to exactly one vertex of $%S. $In this paper, we show that every square stable graph has an efficient dominating set and if a graph has an efficient dominating set, then it is semi square stable. We characterize when the join and the corona product of two disjoint graphs are semi square sable graphs and when they have efficient dominating sets.
Details
- Language :
- English
- ISSN :
- 22518657 and 22518665
- Volume :
- 12
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Transactions on Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.5ef6dda0c32549efb41e143785d4b32b
- Document Type :
- article
- Full Text :
- https://doi.org/10.22108/toc.2022.132784.1967