Graphs with few total dominating sets |
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| Authors: | Marcin Krzywkowski Stephan Wagner |
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| Institution: | 1. Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Poland;2. Department of Mathematical Sciences, Stellenbosch University, South Africa |
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| Abstract: | We give a lower bound for the number of total dominating sets of a graph together with a characterization of the extremal graphs, for trees as well as arbitrary connected graphs of given order. Moreover, we obtain a sharp lower bound involving both the order and the total domination number, and characterize the extremal graphs as well. |
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| Keywords: | Total dominating set Total domination number Subdivided star Lower bound |
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