Divisor 2-Equitable Domination in Fuzzy Graphs

Let \(\mathscr {Q}=(\mathbb {R},\psi ,\varrho )\) be a fuzzy graph. A subset B of \(\mathbb {R}\) is termed as fuzzy equitable dominating set if every \(w \in \mathbb {R}\backslash B ~\exists \) a vertex \(s \in B\ni s w \in \mathscr {E}(\mathscr {Q})\) and \(|d_\mathscr {Q}(s)-d_\mathscr {Q}(w)|\) \(\le 1\) , where \(\mathscr {E}(\mathscr {Q})\) indicates the edge set of \(\mathscr {Q}\) and \(d_\mathscr {Q}(s)\) , \(d_\mathscr {Q}(w)\) indicate the degree of vertices s and w, respectively, and \(\varrho \) (sw) \(\le \psi (s) \wedge \psi (w)\) . A fuzzy equitable dominating sets minimal cardinality indicated by the symbol \(\gamma _{fe}\) . Fuzzy graphs are often utilized in mathematical models of problems due to their simplicity of representation of the relationships between topics. Numerous other fields of study, such as computer science, intelligent systems, psychology, and the medical sciences, have benefited from the dominance of fuzzy graphs. In the overall structure of social networks, an equitable domination has some fascinating applications. Hence, in this research, we have presented creative ideas of divisor 2-equitable dominating set (d2EDS) and exact divisor 2-equitable dominating set (exact d2EDS) in fuzzy graph. The characterizations of minimal divisor 2-equitable domination sets and exact divisor 2-equitable domination sets are discussed.