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Total and paired domination numbers of toroidal meshes

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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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Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their critical commons and helpful suggestions on the original manuscript, and for providing us Ref. (Brešar et al. 2007), which resulted in this version.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, P.R. China

    Fu-Tao Hu

  2. School of Mathematical Sciences, Wentsun Wu Key Laboratory of CAS, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Jun-Ming Xu

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  1. Fu-Tao Hu
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  2. Jun-Ming Xu
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Correspondence to Jun-Ming Xu.

Additional information

The work was supported by NNSF of China (No. 11071233).

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Hu, FT., Xu, JM. Total and paired domination numbers of toroidal meshes. J Comb Optim 27, 369–378 (2014). https://doi.org/10.1007/s10878-012-9519-2

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  • DOI: https://doi.org/10.1007/s10878-012-9519-2

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