Disjoint dominating and total dominating sets in graphs

Authors:
Michael A. Henning;Christian Löwenstein;Dieter Rautenbach;Justin Southey
Affiliations:
Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa;Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany;Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany;Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa
Venue:
Discrete Applied Mathematics
Year:
2010

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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 D@?T necessarily contains all vertices of the graph and that have no induced cycle on five vertices.