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Abstract
Let $G = (V,E)$ be a bipartite graph with partite sets $X$ and $Y$. Two vertices of $X$ are $X$-adjacent if they have a common neighbor in $Y$, and they are $X$-independent otherwise. A subset $D \subseteq X$ is an $X$-outer-independent dominating set of $G$ if every vertex of $X \setminus D$ has an $X$-neighbor in $D$, and all vertices of $X \setminus D$ are pairwise $X$-independent. The $X$-outer-independent domination number of $G$, denoted by $\gamma_X^{oi}(G)$, is the minimum cardinality of an $X$-outer-independent dominating set of $G$. We prove several properties and bounds on the number $\gamma_X^{oi}(G)$.
Authors (2)
-
Yanamandram B. Venkatakrishnan
- Department of Mathematics SASTRA University
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
NATIONAL ACADEMY SCIENCE LETTERS-INDIA
no. 38,
pages 169 - 172,
ISSN: 0250-541X - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Krzywkowski M., Venkatakrishnan Y.: Bipartite theory of graphs: outer-independent domination// NATIONAL ACADEMY SCIENCE LETTERS-INDIA. -Vol. 38, nr. 2 (2015), s.169-172
- Verified by:
- Gdańsk University of Technology
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