Determining vulnerability of central networks using closeness and Nordhaus–Gaddum type relation

The closeness parameter stands as a widely investigated metric within the domain of assessing the stability and vulnerability of intricate network configurations. Within the scope of this inquiry, our focus resided upon the evaluation of closeness values attributed to central graphs, a significant form of graph structure. Our initial pursuit encompassed the computation of closeness values within some special graph structures and their complement graphs of the central graphs. Subsequently, we achieved general outcomes pertaining to central graphs. Ultimately, we furnished a lower-bound for a result of the Nordhaus–Gaddum type.