Malaravan, A. C. & Baskar, A. W. (2021). Both a graph and its complement are self-centered with identical radius. TWMS Journal of Applied and Engineering Mathematics, 11(SI), 240-247.
Abstract
We show that a graph and its complement are self-centered with identical radius r only when r = 2. Further, we provide a construction of such a graph for any given order at least eight.