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An efficient algorithm for distance total domination in block graphs

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Abstract

The \(k\)-distance total domination problem is to find a minimum vertex set \(D\) of a graph such that every vertex of the graph is within distance \(k\) from some vertex of \(D\) other than itself, where \(k\) is a fixed positive integer. In the present paper, by using a labeling method, we design an efficient algorithm for solving the \(k\)-distance total domination problem on block graphs, a superclass of trees.

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Acknowledgments

The authors are grateful to the referees for their valuable suggestions, which result in the present version of the paper. Research was partially supported by the National Nature Science Foundation of China (No. 11171207) and the scientific project for the training of “333” high-level talents in Jiangsu Province.

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Authors and Affiliations

  1. Department of Basic Science, Wuxi City College of Vocational Technology, Jiangsu,  214153, China

    Yancai Zhao

  2. School of Management, Shanghai University, Shanghai,  200444, China

    Erfang Shan

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  1. Yancai Zhao
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  2. Erfang Shan
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Correspondence to Yancai Zhao.

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Zhao, Y., Shan, E. An efficient algorithm for distance total domination in block graphs. J Comb Optim 31, 372–381 (2016). https://doi.org/10.1007/s10878-014-9758-5

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  • DOI: https://doi.org/10.1007/s10878-014-9758-5

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