Partitioning a graph into a dominating set, a total dominating set, and something else

Michael A. Henning; Christian L̈owenstein; Dieter Rautenbach

doi:10.7151/dmgt.1514

Partitioning a graph into a dominating set, a total dominating set, and something else

Michael A. Henning, Christian L̈owenstein, Dieter Rautenbach

Mathematics and Applied Mathematics

Ilmenau University of Technology

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

15 Citations (Scopus)

Abstract

A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159-162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D∪T necessarily contains all vertices of the graph.

Original language	English
Pages (from-to)	563-574
Number of pages	12
Journal	Discussiones Mathematicae - Graph Theory
Volume	30
Issue number	4
DOIs	https://doi.org/10.7151/dmgt.1514
Publication status	Published - 2010

Keywords

Domatic number
Domination
Petersen graph
Total domination
Vertex partition

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.1514

Cite this

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KW - Total domination

KW - Vertex partition

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Partitioning a graph into a dominating set, a total dominating set, and something else

Abstract

Keywords

ASJC Scopus subject areas

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