A novel application by computing partition dimension of subdivision of circulant network

• Published in: IEEE access p. 1
• Main Authors: Nawaz, Rab, Jamil, Muhammad Kamran, Asmat, Farwa, Azeem, Muhammad, Almohsen, Bandar
• Format: Journal Article
• Language: English
• Published: IEEE 2024
• Subjects: Cellular networks; Fault tolerance; Fault tolerant systems; Graph theory; Location awareness; Measurement; Metric resolvability; partition dimension; partition resolving set; Transforms; vertex-based metric resolvability
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2024.3443084

The partition dimension idea was first introduced in the subject of graph theory, primarily for the purpose of analyzing vertex distances. To elaborate, the representation of vertices is subject to certain restrictions in the local partition dimension. The partition dimension of a graph is frequently represented in graph theory as pd ( G ). On the other hand, network localization involves precisely placing nodes in a network with respect to a selected subset, known as the locating set. The smallest size of a network's locating set indicates the network's locating number. For network planning and analysis, the novel framework of the generalized hexagonal cellular network is used. We study the partition dimension of circulant networks and present a complete confirmation of their exact partition dimension. We also look at how the National Disaster Management Authority (NDMA) in Pakistan uses the partition dimension to aid in flood relief efforts. To aid in the rescue of people and animals alike, the NDMA set up relief camps and centers with special codes.