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On the doubly connected domination number of a graph

✍ Scribed by Joanna Cyman; Magdalena Lemańska; Joanna Raczek

Book ID
107385633
Publisher
SP Versita
Year
2006
Tongue
English
Weight
187 KB
Volume
4
Category
Article
ISSN
1895-1074

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The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Graffiti.pc. In part

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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