Minimum Metric Dimension of Generalized Friendship Graphs for Patient Care Monitoring

Patient care during emergencies in healthcare networks faces several challenges such as delays in emergency response, and difficulties in monitoring patients or disease outbreaks across complex systems. The concept of metric dimension in generalized friendship graphs plays a critical role in understanding and managing relationships between key entities within the healthcare networks. In this paper exact value of minimum metric dimension of generalized friendship graphs is calculated to determine monitoring points (landmarks) to ensure effective patient care. Theoretical results and algorithms for the metric dimension of generalized friendship graphs are presented in the context of healthcare networks to efficiently monitor patient flow, trace the spread of infectious diseases, and coordinate emergency responses.