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Classification of Efficient Dominating Sets of Circulant Graphs of Degree 5

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Abstract

For a graph G, a subset D of V(G) is called an efficient dominating set of G if D is an independent set and every vertex in \(V(G) \setminus D\) is adjacent to exactly one vertex in the set D. In this paper, we give necessary and sufficient conditions for the existence of efficient dominating sets of circulant graphs of degree 5 and classify these sets.

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Acknowledgements

The authors are grateful for the referee’s constructive remarks and suggestions. This work was supported by the 2021 Yeungnam University Research Grant. The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2020R1I1A3A04036669).

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Authors and Affiliations

  1. Mathematics, Yeungnam University, Kyongsan, 712-749, Korea

    Young Soo Kwon & Jaeun Lee

  2. Mathematics, Changwon National University, Changwon, 641-773, Korea

    Moo Young Sohn

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  1. Young Soo Kwon
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  2. Jaeun Lee
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  3. Moo Young Sohn
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Correspondence to Moo Young Sohn.

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Kwon, Y.S., Lee, J. & Sohn, M.Y. Classification of Efficient Dominating Sets of Circulant Graphs of Degree 5. Graphs and Combinatorics 38, 120 (2022). https://doi.org/10.1007/s00373-022-02527-6

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  • DOI: https://doi.org/10.1007/s00373-022-02527-6

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