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Disjoint dominating and total dominating sets in graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2010 English Publisher:Elsevier BVJournal:Discrete Applied Mathematics, volume 158, pages 1,615-1,623 (issn: 0166-218X, Copyright policy )
Authors: Christian Löwenstein; Dieter Rautenbach; Justin Southey; Michael A. Henning;

doi: 10.1016/j.dam.2010.06.004

Disjoint dominating and total dominating sets in graphs

Abstract

AbstractIt has been shown [M.A. Henning, J. Southey, A note on graphs with disjoint dominating and total dominating sets, Ars Combin. 89 (2008) 159–162] that every connected graph with minimum degree at least two that is not a cycle on five vertices has a dominating set D and a total dominating set T which are disjoint. We characterize such graphs for which D∪T necessarily contains all vertices of the graph and that have no induced cycle on five vertices.

Related Organizations
Keywords

Total domination, Applied Mathematics, Discrete Mathematics and Combinatorics, Vertex partition, Domination

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
21
Top 10%
Top 10%
Top 10%
hybrid