31914 Applications of Split Divisor Equitable Domination in Fuzzy Graphs to Network Theory

Split equitable domination equitable domination aims to ensure that every partition of the network is fairly served by its dominating set, promoting fairness in coverage, resource allocation, and influence distribution. This concept has practical implications in various domains, including urban infrastructure planning, resource allocation in social networks, and load balancing in computer networks. In a communication network represented by a network graph, it is important to identify key nodes that form an equitable dominating set to efficiently manage the network. These key nodes should be able to ensure network connectivity and prevent a single point of failure. By removing these key nodes, the network should split into smaller, manageable sub-networks to maintain network resilience and reliability. A graph is split dominant if removing its dominating set disconnects the graph. In this article, we discuss split divisor equitable dominating sets in fuzzy graphs, including the definitions of split divisor equitable domination divisor equitable domination number and split divisor minimal equitable dominating set. We also explore the characterizations of minimal fuzzy split divisor equitable dominating set and the relationship between minimum split divisor equitable dominating set and maximal split divisor equitable dominating set.