Graphs of Extremal Weights

Béla Bollobdés1, Paul Erdos2
1 Department of Pure Mathematics and Mathematical Statistics University of Cambridge 16 Mill Lane Cambridge CB3 9AX England
2Mathematical Institute of the Hungarian Academy of Sciences Redltanoda utca 13-15 Budapest H-1053 Hungary

Abstract

Our main aim is to show that the Randi\’e weight of a connected graph of order \(n\) is at least \(\sqrt{n – 1}\). As shown by the stars, this bound is best possible.