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Bounds on the -domination number of a graph

✍ Scribed by Ermelinda DeLaViña; Wayne Goddard; Michael A. Henning; Ryan Pepper; Emil R. Vaughan

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
200 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

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 particular, we show that for any graph with minimum degree at least 2k -1, the k-domination number is at most the matching number.

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