Disjoint dominating and total dominating sets in graphs |
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| Authors: | Michael A Henning Justin Southey |
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| Institution: | a Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africab Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany |
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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. |
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| Keywords: | Domination Total domination Vertex partition |
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