Radio mean labeled paths in Cryptography

Graph coloring or labeling is an NP-complete problem. The labeling technique in the scope of this paper is radio mean labeling. We integrate the radio mean labeling of graphs with the encryption/decryption process using matrices. An intruder can easily crack the secret message if the matrix or its inverse is known. The unique radio mean number of a graph is used to construct the key matrix for encryption. The inverse of this matrix is then the matrix for decryption. Out of all graphs of a given order, graphs isomorphic to path graphs have the maximum diameter. Since the mathematical constraint associated with the radio mean labeling of any given graph depends solely on the graph’s order and diameter, deriving the radio mean number of paths is difficult as order increases. Hence, we choose path graphs for constructing the key matrix for encryption.