Difference divisor labeling for graph-based cryptographic applications: a novel approach to secure encoding

This study introduces a novel labeling scheme to graph theory known as Difference Divisor Labeling that is aimed at
facilitating cryptographic applications through an edge labeling based in mathematics. This method labels the vertices
based on the divisors of a positive integer, and then obtains the edge labels based on the parity and/or difference of the
adjacent vertices. There are a number of distinct and significant advantages of this labeling paradigm over traditional
graph labeling algorithms, which tend to have constraints on applicability, scalability, and flexibility for dealing with
complicated or irregular graphs. Difference Divisor Labeling is applied and demonstrated on a variety of classes of graphs,
specifically cycle graphs, regular graphs, and complete bipartite graphs, to show that they all meet the specifications of
the proposed labeling. The labeled edge values are used as plaintext to encrypt with affine and RSA ciphers, highlighting
to the reader the goal of building some secure graph-based cryptographic system. The paper describes full encryption
and decryption methods for both types of graphs, and demonstrates how the labeling can ensure unpredictable and secure
ciphertext generation. By exceeding the limitations of traditional labelings and being easily integrated with newer cryptographic
algorithms, Difference Divisor Labeling represents a versatile and secure communication platform in the digital
networks. This will open innovative paths of graph-theoretic encryption as it converges discrete mathematical abstractions
and concepts of information security.