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On the r-domination number of a graph

✍ Scribed by Jerrold R. Griggs; Joan P. Hutchinson

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 468 KB
Volume: 101
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90591-3

No coin nor oath required. For personal study only.

✦ Synopsis

For r > 0, let the r-domination number of a graph, d,, be the size of a smallest set of vertices such that every vertex of the graph is within distance r of a vertex in that set. This paper contains proofs that every graph with a spanning tree with at least n/2 leaves has d, s n/(2r); this compares with the easy upper bound of [n/(2r + 1)1 for graphs with Hamiltonian paths.

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