# A Note on Non-Dominating Set Partitions in Graphs

Wyatt J. Desormeaux; Teresa W. Haynes; Michael A. Henning

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 4, page 1043-1050
- ISSN: 2083-5892

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topWyatt J. Desormeaux, Teresa W. Haynes, and Michael A. Henning. "A Note on Non-Dominating Set Partitions in Graphs." Discussiones Mathematicae Graph Theory 36.4 (2016): 1043-1050. <http://eudml.org/doc/287166>.

@article{WyattJ2016,

abstract = {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.},

author = {Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; total domination; non-dominating partition; nontotal dominating partition},

language = {eng},

number = {4},

pages = {1043-1050},

title = {A Note on Non-Dominating Set Partitions in Graphs},

url = {http://eudml.org/doc/287166},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Wyatt J. Desormeaux

AU - Teresa W. Haynes

AU - Michael A. Henning

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

JO - Discussiones Mathematicae Graph Theory

PY - 2016

VL - 36

IS - 4

SP - 1043

EP - 1050

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/287166

ER -

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