Domination in Fuzzy Directed Graphs

Enrico Enriquez, Grace Estrada, Carmelita Loquias, Reuella J Bacalso and Lanndon Ocampo
Additional contact information
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

Mathematics, 2021, vol. 9, issue 17, 1-14

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.

Keywords: dominating set; digraph; fuzzy graph; fuzzy digraph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/17/2143/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/17/2143/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:17:p:2143-:d:627929

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().