Elsevier

Discrete Applied Mathematics

Volume 158, Issue 15, 6 August 2010, Pages 1615-1623
Discrete Applied Mathematics

Disjoint dominating and total dominating sets in graphs

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Abstract

It 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 DT necessarily contains all vertices of the graph and that have no induced cycle on five vertices.

Keywords

Domination
Total domination
Vertex partition

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