Year 2015

• 2-outer-independent domination in graphs

  Publication

  • N. Jafari Rad
  • M. Krzywkowski

  - NATIONAL ACADEMY SCIENCE LETTERS-INDIA - Year 2015

  We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...

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• Bipartite theory of graphs: outer-independent domination

  Publication

  • M. Krzywkowski
  • Y. B. Venkatakrishnan

  - NATIONAL ACADEMY SCIENCE LETTERS-INDIA - Year 2015

  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...

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