Optimizing Network Connectivity via Fuzzy Hub Domination

Abstract

This work studies hub domination and total hub domination in both standard and fuzzy graphs. We determine exact values for principal graph families (paths, cycles, complete graphs, complete bipartite graphs, and wheels) and develop structural bounds that relate hub parameters to classical invariants. On the fuzzy side, we formalize hub domination with vertex and edge memberships, compute the fuzzy hub domination number for standard fuzzy graph classes, and derive degree- and structure-based bounds. We connect these results to applications in telecommunication and transportation networks, where minimizing hub cost aligns with the fuzzy hub domination objective. The findings clarify the mathematical structure of hub domination, situate it among core graph-theoretic measures, and provide implementable bounds and algorithms for design under uncertainty. These contributions offer tools for cost-aware hub placement and resilient connectivity in complex networks modeled by fuzzy graphs.