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
- dr inż. Marcin Krzywkowski link open in new tab ,
- Yanamandram B. Venkatakrishnan
Additional information
- Category
- Publikacja w czasopiśmie
- Type
- artykuł w czasopiśmie wyróżnionym w JCR
- Language
- angielski
- Publication year
- 2015
