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Dominating Broadcasts in Fuzzy Graphs

Author

Listed:
  • Passawan Noppakaew

    (Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand
    These authors contributed equally to this work.)

  • Kaewkan Hengthonglert

    (Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand)

  • Sawanya Sakuntasathien

    (Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand
    These authors contributed equally to this work.)

Abstract

Broadcasting problems in graph theory play a significant role in solving many complicated physical problems. However, in real life there are many vague situations that sometimes cannot be modeled using usual graphs. Consequently, the concept of a fuzzy graph G F : ( V , σ , μ ) has been introduced to deal with such problems. In this study, we are interested in defining the notion of dominating broadcasts in fuzzy graphs. We also show that, in a connected fuzzy graph containing more than one element in σ * , a dominating broadcast always exists, where σ * is { v ∈ V | σ ( v ) > 0 } . In addition, we investigate the relationship between broadcast domination numbers, radii, and domination numbers in a fuzzy graph as follows; γ b ( G F ) ≤ min { r ( G F ) , γ ( G F ) } , where γ b ( G F ) is the broadcast domination number, r ( G F ) is the radius, and γ ( G F ) is domination numbers in fuzzy graph G F , with | σ * | > 1 .

Suggested Citation

  • Passawan Noppakaew & Kaewkan Hengthonglert & Sawanya Sakuntasathien, 2022. "Dominating Broadcasts in Fuzzy Graphs," Mathematics, MDPI, vol. 10(2), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:281-:d:726770
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    Cited by:

    1. Hao Guan & Waheed Ahmad Khan & Amna Fida & Khadija Ali & Jana Shafi & Aysha Khan, 2024. "Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs," Mathematics, MDPI, vol. 12(6), pages 1-14, March.

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