Domination, radius, and minimum degree

We prove sharp bounds concerning domination number, radius, order and minimum degree of a graph. In particular, we prove that if image is a connected graph of order image, domination number image and radius image, then image. Equality is achieved in the upper bound if, and only if, image is a path or a cycle on image vertices with image. Further, if image has minimum degree image and image, then using a result due to Erdös, Pach, Pollack, and Tuza [P. Erdös, J. Pach, R. Pollack, Z. Tuza, Radius, diameter, and minimum degree. J. Combin. Theory B 47 (1989), 73–79] we show that image.