Domination, radius, and minimum degree

Abstract: We prove sharp bounds concerning domination number, radius, order and minimum degree of a graph. In particular, we prove that if is a connected graph of order , domination number and radius , then . Equality is achieved in the upper bound if, and only if, is a path or a cycle on vertices with . Further, if has minimum degree and , 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 . [Copyright &y& Elsevier]