Novel Domination Parameter in Fuzzy Graph Theory Based on K-Integrity Measures

Abstract

This paper proposes a novel domination parameter in fuzzy graph theory, termed the -integrity fuzzy domination number, denoted by . The parameter is defined as the minimum cardinality of a vertex subset  such that the aggregated minimum fuzzy adjacency from each member of  to all vertices in the graph satisfies the threshold condition: . This approach combines structural control with fuzzy membership power, improving the traditional domination model by considering how it can be made stronger in uncertain situations.