Enrico Enriquez, Grace Estrada, Carmelita Loquias, Reuella J. Bacalso, Lanndon Ocampo
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 GD = (σD, µD) is a pair of two functions σD: V → [0, 1] and µD: A → [0, 1], such that µD((x, y)) ≤ σD(x) ∧ σD(y), where x, y ∈ V. An edge µD((x, y)) of a fuzzy digraph is called an effective edge if µD((x, y)) = σD(x) ∧ σD(y). Let x, y ∈ V. The vertex σD(x) dominates σD(y) in GD if µD ((x, y)) is an effective edge. Let S ⊆ V, u ∈ V\S, and v ∈ S. A subset σD(S) ⊆ σD is a dominating set of GD if, for every σD(u) ∈ σD\σD(S), there exists σD(v) ∈ σD(S), such that σD(v) dominates σD(u). The minimum dominating set of a fuzzy digraph GD is called the domination number of a fuzzy digraph and is denoted by γ(GD). 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. © 2021 by the authors.
Department of Computer, Information Science and Mathematics, University of San Carlos, Cebu City, 6000, Philippines; 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
