• Hülya Gür
• Yılmaz Gür

This study has been undertaken to investigate the determinants of stock returns in Karachi Stock Exchange (KSE) using two assets. This paper seeks to develop a new encryption method which applies the intersection of graph theory and cryptography using cycles within complete graphs for both message encryption and ciphertext generation. To understand the cycles in Hamiltonian complete graphs, the focus will be on the components of complete graphs and cycles and their corresponding roles in the processes of encryption and decryption. To ensure confidential and secure transmission of data, various encryption techniques are employed. One such approach implements concepts from graph theory such as vertices, edges, weighted graphs, complete graphs, and Hamiltonian cycles. In this scenario, vertices and edges represent the basic building blocks for ascribing and comprehending the skeleton framework of the encryption algorithm which is known to be of a high level of sophistication. In the domain of cryptology, Hamiltonian cycles are crucial for creating secure keys and for advanced encryption that require strong anti-encryption techniques. The process outlined assures that the information being sent will remain secure against unauthorized access and modification since the key guarantees confidentiality and integrity of the information. The use of a complete graph serves an integral role in the encryption process and Hamiltonian cycles provide a secure structure for key generations.

Graph theory, cryptography, encryption, complete graph-Hamiltonian cycles

"Graph Theory Based Encryption: Leveraging Complete Graphs and Hamiltonian Cycles for Secure Communication ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 5, page no.h514-h521, May-2025, Available :http://www.jetir.org/papers/JETIR2505849.pdf

"Graph Theory Based Encryption: Leveraging Complete Graphs and Hamiltonian Cycles for Secure Communication ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 5, page no. pph514-h521, May-2025, Available at : http://www.jetir.org/papers/JETIR2505849.pdf