A Note on Non-Dominating Set Partitions in Graphs

• Autorzy: Wyatt J. Desormeaux , Teresa W. Haynes , Michael A. Henning
• Języki publikacji: EN

Abstrakty

EN

A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non-dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating) sets is a non-dominating (non-total dominating) set partition. We show that the minimum number of sets in a non-dominating set partition of a graph G equals the total domination number of its complement G̅ and the minimum number of sets in a non-total dominating set partition of G equals the domination number of G̅ . This perspective yields new upper bounds on the domination and total domination numbers. We motivate the study of these concepts with a social network application.

Słowa kluczowe

EN

domination; total domination; non-dominating partition; nontotal dominating partition

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 4
• Strony: 1043-1050

Daty

wydano

2016-11-01

otrzymano

2015-08-12

poprawiono

2016-01-23

zaakceptowano

2016-01-26

online

2016-10-21

Twórcy

autor

Wyatt J. Desormeaux

• Research supported in part by the University of Johannesburg
• Department of Mathematics, University of Johannesburg Auckland Park, 2006,

autor

Teresa W. Haynes

• Research supported in part by the University of Johannesburg
• Department of Mathematics, University of Johannesburg Auckland Park, 2006 South Africa
• Department of Mathematics and Statistics East Tennessee State University Johnson City, TN 37614-0002,

autor

Michael A. Henning

• Research supported in part by the University of Johannesburg and the South African National Research Foundation
• Department of Mathematics, University of Johannesburg Auckland Park, 2006,

Identyfikatory

DOI

10.7151/dmgt.1895