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Subdomination in Graphs with Upper-Bounded Vertex Degree

Author

Listed:
  • Darya Lemtyuzhnikova

    (V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

  • Pavel Chebotarev

    (Technion—Israel Institute of Technology, Haifa 3200003, Israel
    A.A. Kharkevich Institute for Information Transmission Problems of RAS, 127051 Moscow, Russia)

  • Mikhail Goubko

    (V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

  • Ilja Kudinov

    (V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

  • Nikita Shushko

    (V.A. Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

Abstract

We find a lower bound for the k -subdomination number on the set of graphs with a given upper bound for vertex degrees. We study the cases where the proposed lower bound is sharp, construct the optimal graphs and indicate the corresponding k -subdominating functions. The results are interpreted in terms of social structures.

Suggested Citation

  • Darya Lemtyuzhnikova & Pavel Chebotarev & Mikhail Goubko & Ilja Kudinov & Nikita Shushko, 2023. "Subdomination in Graphs with Upper-Bounded Vertex Degree," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2722-:d:1172083
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