Comparative Study of Antimagic Labeling Approaches in Wireless, Interconnection, and Smart Grid Networks

The antimagic labeling of a graph is an important factor of graph theory, which implies the assignment of individual integer values to the graph’s vertices such that all the vertex sums remain unique. Due to the distinctive feature of antimagic labeling, there has been considerable interest in the scientific world, as well as real-world graph applications, leading us to engage in a comparative study of local antimagic labeling, edge antimagic labeling, PRIME antimagic labeling, and fuzzy antimagic labeling, particularly for their uses in wireless sensor networks, interconnection networks, and power management systems, respectively. However, the different approaches have varying mathematical foundations for their implementations or strategies, such as constructive labeling methods, number theory–based PRIME algorithm implementations, or even fuzzy modeling. Several crucial parameters are also important for evaluating these labeling schemes for networks. For instance, a tested evaluation has demonstrated that all the labeling schemes have different merits depending upon a specific network topology or application requirements. For instance, the discussion emphasizes that no labeling approach can be judged as optimum for a specific application by considering the choice of antimagic labeling schemes for the optimization of advanced networks.