Total and paired domination numbers of toroidal meshes |
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Authors: | Fu-Tao Hu Jun-Ming Xu |
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Affiliation: | 1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, P.R. China 2. School of Mathematical Sciences, Wentsun Wu Key Laboratory of CAS, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China
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Abstract: | Let G be a graph without isolated vertices. The total domination number of G is the minimum number of vertices that can dominate all vertices in G, and the paired domination number of G is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching. This paper determines the total domination number and the paired domination number of the toroidal meshes, i.e., the Cartesian product of two cycles C n and C m for any n≥3 and m∈{3,4}, and gives some upper bounds for n,m≥5. |
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