Bounds on the k -domination number of a graph

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 pa...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Applied mathematics letters 2011-06, Vol.24 (6), p.996-998
Hauptverfasser: DeLaViña, Ermelinda, Goddard, Wayne, Henning, Michael A., Pepper, Ryan, Vaughan, Emil R.
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-domination
Computer programs
Exact sciences and technology
Graph
Graphs
Independence number
Matching
Matching number
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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 2 k − 1 , the k -domination number is at most the matching number.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2011.01.013