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Lower bound on the distance $k$-domination number of a tree

In: Mathematica Slovaca, vol. 56, no. 2
Joanna Raczek - Joanna Cyman

Details:

Year, pages: 2006, 235 - 243
About article:
A subset $D$ of vertices of a graph $G=(V,E)$ is said to be a distance $k$-dominating set of $G$ if every vertex of $V-D$ is at distance at most $k$ from some vertex of $D$. The minimum size of a distance $k$-dominating set of $G$ is called the distance $k$-domination number of $G$. We prove that for each tree $T$ of order $n$ with $n1$ end-vertices, the distance $k$-domination number is bounded below by $(n+2k-k· n1)/(2k+1)$ and we characterize the corresponding extremal trees.
How to cite:
ISO 690:
Raczek, J., Cyman, J. 2006. Lower bound on the distance $k$-domination number of a tree. In Mathematica Slovaca, vol. 56, no.2, pp. 235-243. 0139-9918.

APA:
Raczek, J., Cyman, J. (2006). Lower bound on the distance $k$-domination number of a tree. Mathematica Slovaca, 56(2), 235-243. 0139-9918.