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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2016 | 36 | 4 | 1043-1050

## A Note on Non-Dominating Set Partitions in Graphs

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.

EN

1043-1050

wydano
2016-11-01
otrzymano
2015-08-12
poprawiono
2016-01-23
zaakceptowano
2016-01-26
online
2016-10-21

### Twórcy

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