Graph Associated to a Fuzzy Hypergroupoid

In this paper, our aim is to study the graph associated to a fuzzy hypergroupoids(hypergroup). For a (S, ∘) is a fuzzy hypergroup, we associate a graph Γ_S to S, such that its vertices are the elements of S and two distinct vertices x and y are adjacent if xαy , where α is a relation on S, with transitive closure α*, is the smallest equivalence relation on S, such that the quotient space(S/ α *, ⊗) is a groupoid (group). We will proceed to study the relationship between algebraic properties of (S, ∘) and graph theoretic properties of graph Γ_S. Finally, we apply the graph Γ_S are advanced in COVID-19 context to modeling this phenomenon.In this paper, our aim is to study the graph associated to a fuzzy hypergroupoids(hypergroup). For a (S, ∘) is a fuzzy hypergroup, we associate a graph Γ_S to S, such that its vertices are the elements of S and two distinct vertices x and y are adjacent if xαy , where α is a relation on S, with transitive closure α*, is the smallest equivalence relation on S, such that the quotient space(S/ α *, ⊗) is a groupoid (group). We will proceed to study the relationship between algebraic properties of (S, ∘) and graph theoretic properties of graph Γ_S. Finally, we apply the graph Γ_S are advanced in COVID-19 context to modeling this phenomenon.