Domination in Fuzzy Directed Graphs

Enrico Enriquez, Grace Estrada, Carmelita Loquias, Reuella J Bacalso and Lanndon Ocampo
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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 = ? D , ? D is a pair of two functions ? D : V ? 0 , 1 and ? D : A ? 0 , 1 , such that ? D x , y ? ? D x ? ? D y , where x , y ? V . An edge ? D x , y of a fuzzy digraph is called an effective edge if ? D x , y = ? D x ? ? D y . Let x , y ? V . The vertex ? D x dominates ? D y in G D if ? D x , y is an effective edge. Let S ? V , u ? V \ S , and v ? S . A subset ? D S ? ? D is a dominating set of G D if, for every ? D u ? ? D \ ? D S , there exists ? D v ? ? D S , such that ? D v dominates ? 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 ? 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)

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