Abstract: Modern Communication systems require network security in order to provide safe data transfer, efficient routing and fault tolerance measures. Total Prime Graceful labeling facilitates the identification of security threats within the network infrastructure. Total Prime Graceful labeling is an intriguing concept in graph theory that has applications in many different domains because of its special qualities and possible uses. The practical uses of total prime graceful labeling in diverse domains of network security contexts are examined in this study.


Keywords: Total Prime Graceful Labeling, Star Graph, SIEM, VPN, Access Control Systems