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Semi square stable graphs and efficient dominating sets | ||
| Transactions on Combinatorics | ||
| دوره 12، شماره 2، شهریور 2023، صفحه 107-113 اصل مقاله (967.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.132784.1967 | ||
| نویسندگان | ||
| Baha̓ Abughazaleh* ؛ Omar Abughneim | ||
| Department of Mathematics, Faculty of Science, Isra, University,, Amman, Jordan | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| independence number؛ independent dominating number؛ efficient dominating sets؛ semi square stable graphs؛ graph operations | ||
| مراجع | ||
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[7] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Monographs and Text- books in Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998. [8] V. E. Levit and E. Mandrescu, Square-stable and well-covered graphs, Acta Universitatis Apulensis, 10 (2015) 297–308. [9] B. Randerath and L. Volkmann, Simplicial graphs and relationships to different graph invariants, Ars Combin., 46 (1997) 211–217. [10] W. Willis, Bounds for the independence number of a graph, Master Thesis in Virginia Commonwealth University, 2011. | ||
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آمار تعداد مشاهده مقاله: 181 تعداد دریافت فایل اصل مقاله: 187 |
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