Some results on universal minimal total dominating functions |
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| Authors: | Fang Qizhi Cai Maocheng |
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| Affiliation: | (1) Department of Applied Mathematics, Qingdao Ocean University, 266003 Qingdao, China;(2) Institute of Systems Science, the Academy of Mathematics and Systems Sciences, the Chinese Academy of Sciences, 100080 Beijing, China |
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| Abstract: | In this paper, we introduce the concepts of redundant constraint and exceptional vertex which play an important role in the characterization of universal minimal total dominating functions (universal MTDFs), and establish some further results on universal MTDFs in general graphs. By extending these results to trees, we get a necessary and sufficient condition for universal MTDFs and show that there is a good algorithm for deciding whether a given tree has a universal MTDF. |
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| Keywords: | Total dominating function (TDF) minimal TDF (MTDF) universal MTDF redundant constraint exceptional vertex |
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