Application of Graph theory to Defend Hypercubes and Matching Graph of Hypercube Structures Against Cyber Threats

Cyber security is the key threat and is of primary concern since the outbreak of the pandemic events of COVID-19. Hypercube network topology known for its unique message-passing capabilities, present promising avenues for constructing robust and secure communication systems. To fortify these networks against cyber threats, graph vertex cover techniques have emerged as effective defense mechanisms. In this article, the applications of graph covering, specifically vertex covering and edge covering, for hypercubes, matching graph of hypercubes and line graphs of hypercube networks is focused. These covering techniques can be strategically applied to identify critical nodes and edges, offering enhanced protection against potential cyber-attacks. By analyzing and optimizing the selection of covering sets, more resilient hypercube-based communication infrastructures that can withstand and mitigate cyber threats can be developed effectively. Through this study the ongoing efforts in building secure and trustworthy network environments in the face of ever-evolving cyber threats is accomplished.