Some Graph Based Encryption Techniques

In today’s fast-evolving technological environment, ensuring confidentiality is of utmost importance. Cryptography stands as a critical discipline in safeguarding information from unauthorized access. It employs various encryption algorithms to secure data effectively. As digital threats evolve, there’s a growing demand for unconventional encryption methods to counter traditional cyber-attacks. This paper introduces innovative encryption algorithms leveraging special graphs and public key cryptography techniques, enhancing security through modular arithmetic properties and enabling more robust communication safeguards. A partition V₁, V₂,…, V_k of the vertex set V is called a chromatic partition of G if each Vi, 1 ≤ i ≤ k is an independent set of G. The minimum order of a chromatic partition of G is called chromatic number χ(G). A chromatic partition of G is called an ordered partition if |V₁| = β₀ and |V_i| = β₀(V − ∪_j=1ⁱ V_j ). The order of a minimum ordered chromatic partition of G is called ordered chromatic number χ₁(G). It is immediate that χ₁(G) ≥ χ(G). In this paper we extend Nordhaus Gaddum results to ordered chromatic number.