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Domination in Fuzzy Directed Graphs

Author

Listed:
  • Enrico Enriquez

    (Department of Computer, Information Science and Mathematics, University of San Carlos, Cebu City 6000, Philippines)

  • Grace Estrada

    (Department of Computer, Information Science and Mathematics, University of San Carlos, Cebu City 6000, Philippines)

  • Carmelita Loquias

    (Department of Computer, Information Science and Mathematics, University of San Carlos, Cebu City 6000, Philippines)

  • Reuella J Bacalso

    (Department of Computer, Information Science and Mathematics, University of San Carlos, Cebu City 6000, Philippines)

  • Lanndon Ocampo

    (Department of Industrial Engineering, Cebu Technological University, Cebu City 6000, Philippines
    Center for Applied Mathematics and Operations Research, Cebu Technological University, Cebu City 6000, Philippines)

Abstract

A new domination parameter in a fuzzy digraph is proposed to espouse a contribution in the domain of domination in a fuzzy graph and a directed graph. Let G D * = V , A be a directed simple graph, where V is a finite nonempty set and A = x , y : x , y ∈ V , x ≠ y . A fuzzy digraph G D = σ D , μ D is a pair of two functions σ D : V → 0 , 1 and μ D : A → 0 , 1 , such that μ D x , y ≤ σ D x ∧ σ D y , where x , y ∈ V . An edge μ D x , y of a fuzzy digraph is called an effective edge if μ D x , y = σ D x ∧ σ D y . Let x , y ∈ V . The vertex σ D x dominates σ D y in G D if μ D x , y is an effective edge. Let S ⊆ V , u ∈ V \ S , and v ∈ S . A subset σ D S ⊆ σ D is a dominating set of G D if, for every σ D u ∈ σ D \ σ D S , there exists σ D v ∈ σ D S , such that σ D v dominates σ D u . The minimum dominating set of a fuzzy digraph G D is called the domination number of a fuzzy digraph and is denoted by γ G D . In this paper, the concept of domination in a fuzzy digraph is introduced, the domination number of a fuzzy digraph is characterized, and the domination number of a fuzzy dipath and a fuzzy dicycle is modeled.

Suggested Citation

  • Enrico Enriquez & Grace Estrada & Carmelita Loquias & Reuella J Bacalso & Lanndon Ocampo, 2021. "Domination in Fuzzy Directed Graphs," Mathematics, MDPI, vol. 9(17), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2143-:d:627929
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    References listed on IDEAS

    as
    1. Yue, Jun & Wei, Meiqin & Li, Min & Liu, Guodong, 2018. "On the double Roman domination of graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 669-675.
    2. Abdollahzadeh Ahangar, H. & Álvarez, M.P. & Chellali, M. & Sheikholeslami, S.M. & Valenzuela-Tripodoro, J.C., 2021. "Triple Roman domination in graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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    Citations

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    Cited by:

    1. Narayanan Kumaran & Annamalai Meenakshi & Miroslav Mahdal & Jayavelu Udaya Prakash & Radek Guras, 2023. "Application of Fuzzy Network Using Efficient Domination," Mathematics, MDPI, vol. 11(10), pages 1-20, May.

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