A note on graphs with disjoint dominating and total dominating sets

Michael A. Henning; Justin Southey

A note on graphs with disjoint dominating and total dominating sets

Michael A. Henning, Justin Southey

University of KwaZulu-Natal

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this note, we show that the vertex set of every graph with minimum degree at least two and with no component that is a 5-cycle can be partitioned into a dominating set and a total dominating set.

Original language	English
Pages (from-to)	159-162
Number of pages	4
Journal	Ars Combinatoria
Volume	89
Publication status	Published - Oct 2008
Externally published	Yes

Keywords

Domination
Total domination
Vertex partition

ASJC Scopus subject areas

General Mathematics

Cite this

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AB - A total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this note, we show that the vertex set of every graph with minimum degree at least two and with no component that is a 5-cycle can be partitioned into a dominating set and a total dominating set.

KW - Domination

KW - Total domination

KW - Vertex partition

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M3 - Article

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JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

A note on graphs with disjoint dominating and total dominating sets

Abstract

Keywords

ASJC Scopus subject areas

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Cite this