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

In: Mathematica Slovaca, vol. 56, no. 2
Joanna Raczek - Joanna Cyman
Detaily:
Rok, strany: 2006, 235 - 243
O článku:
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.
Ako citovať:
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.