EPIDEMIC CONTACT TRACING AND CONTAINMENT IN FUZZY SOCIAL GRAPHS USING STRENGTH-BASED FUZZY LOCATION TOTAL DOMINATION SETS

Abstract

In this study, we investigate the concept of fuzzy locating total dominating sets (FLTDS) in simple connected fuzzy graphs. A subset   is defined as a FLTDS if every

 if each vertex outside of  is next to at least one  vertex via a strong arc (fuzzy domination), and each such vertex has a unique strength-based representation vector with respect to  (fuzzy locating property). The strength-based representation captures the degrees of connectivity between a vertex and the elements of the dominating set, reflecting the inherent fuzziness of relationships in the graph. We define the fuzzy locating total domination number  as the minimum cardinality of a FLTDS in a fuzzy graph ​. The paper presents foundational results and characterizations of FLTDS in selected classes of fuzzy graphs, providing insights into their structural properties and potential applications in network monitoring, fault detection, and information spread in uncertain environments