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The Outer-connected Domination Number of Sierpiński-like Graphs

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Abstract

An outer-connected dominating set in a graph G = (V, E) is a set of vertices D ⊆ V satisfying the condition that, for each vertex v ∉ D, vertex v is adjacent to some vertex in D and the subgraph induced by V∖D is connected. The outer-connected dominating set problem is to find an outer-connected dominating set with the minimum number of vertices which is denoted by \(\tilde {\gamma }_{c}(G)\). In this paper, we determine \(\tilde {\gamma }_{c}(S(n,k))\), \(\tilde {\gamma }_{c}(S^{+}(n,k))\), \(\tilde {\gamma }_{c}(S^{++}(n,k))\), and \(\tilde {\gamma }_{c}(S_{n})\), where S(n, k), S +(n, k), S ++(n, k), and S n are Sierpi\(\acute {\mathrm {n}}\)ski-like graphs.

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Acknowledgments

The authors would like to thank anonymous referees for their careful reading with corrections and useful comments which helped to improve the paper.

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Authors and Affiliations

  1. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan

    Shun-Chieh Chang & Yue-Li Wang

  2. Department of Information Management, Shih Hsin University, Taipei, Taiwan

    Jia-Jie Liu

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  1. Shun-Chieh Chang
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  2. Jia-Jie Liu
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  3. Yue-Li Wang
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Correspondence to Yue-Li Wang.

Additional information

This work was supported in part by the National Science Council of Republic of China under contracts NSC 100–2221–E–011–067-MY3, NSC 101–2221–E–011–038–MY3, NSC 100-2221-E-011-068-, and NSC 100-2221-E-128-003-.

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Chang, SC., Liu, JJ. & Wang, YL. The Outer-connected Domination Number of Sierpiński-like Graphs. Theory Comput Syst 58, 345–356 (2016). https://doi.org/10.1007/s00224-015-9621-9

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  • DOI: https://doi.org/10.1007/s00224-015-9621-9

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