Year 2014

• Bounds on the vertex-edge domination number of a tree

  Publication

  • B. Krishnakumari
  • Y. B. Venkatakrishnan
  • M. Krzywkowski

  - COMPTES RENDUS MATHEMATIQUE - Year 2014

  A vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...

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Year 2011

• A lower bound on the total outer-independent domination number of a tree

  Publication

  • M. Krzywkowski

  - COMPTES RENDUS MATHEMATIQUE - Year 2011

  A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...

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• An upper bound on the 2-outer-independent domination number of a tree

  Publication

  • M. Krzywkowski

  - COMPTES RENDUS MATHEMATIQUE - Year 2011

  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 a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...

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