Bounds on the k-domination number of a graph

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.

• Type: Journal
• Year: 2011
• Where: APPML
• Authors: Ermelinda DeLaViña, Wayne Goddard, Michael A. Henning, Ryan Pepper, Emil R. Vaughan
• Keywords: APPML 2011, K-domination Number, Matching Number, Minimum Degree, Software Engineering