Application of Graph Complements and Labeling in Secure Communication

The internet has become a permanent fixture in people’s lives and has expanded significantly over the last few decades. As it has grown, data protection has become a critical concern to ensure that information is accessed only by intended recipients and remains secure from unauthorized modifications. Encryption plays a crucial role in data protection by transforming information into an unreadable format using a specific algorithm, requiring proper decryption to access and utilize the data. Graph theory, a field within discrete mathematics, is widely applied to strengthen encryption techniques for securing information. Harmonious labeling is utilized to assign values to edges in a graph, representing encrypted plaintext to ensure secure communication. Furthermore, incorporating the complement of a graph method along with the partial complement enhances encryption by adding an extra layer of complexity.