On Some Bounds of Fuzzy Secure Domination Number - Joy, Mariya C.; Isaac, Paul (Communications in Mathematics and Applications, 2025)
In a fuzzy graph \(G_f(ρ, η)\) with vertex set \(V\), a subset \(D \subseteq V\) is called a dominating set if each vertex in the graph is either a member of \(D\) or has at least one strong neighbor in \(D\). A secure dominating set \(S\) is a dominating set with the additional property that every vertex outside \(S\) has a strong neighbor in \(S\), that can swap places with it and still maintain domination. The minimum fuzzy cardinality of such secure dominating sets is called the secure domination number, denoted \(γ_{sc}(G_f)\). This paper explores bounds for the fuzzy secure domination number and examines its relationship with the domination number, independence number, and matching number.
Keywords: Fuzzy graphs; Fuzzy secure domination; Fuzzy secure total domination; Fuzzy secure total domination number