A study on various domination parameters of graphs and its applications in science and engineering

Abstract

An interconnection network comprises two or more computers linked to share resources (such as routers and printers), exchange information, or facilitate digital conversations. Cables, phone lines, satellites, radio waves, or infrared laser beams are all examples of connections that a network can make to its computers. Imagine that we wish to use one or a few computers to monitor the activities of each computer in such a way that each computer has control over its neighbours. Graph theory refers to these controllers as a dominating (vertex) set. In this situation, several questions inevitably arise. The smallest dominating set offers the solution when the monitoring effort of the network needs to be lowered. It is worth investigating the minimum number of computers necessary to monitor the communication network fully. In coding theory and computer science, computing the domination number for an r-dimensional hypercube is significant. In computer science, domination invariants can be used to highlight various types of interconnection network vulnerabilities, with hypercubes acting as a critical model for interconnection networks. Domination is vital in a multitude of domains, including communications, biological models, facility positioning problems, chemistry, and social networks. newline