Note on graphs without repeated cycle lengths

In this note we prove that every 2-connected graph of order n with no repeated cycle lengths has at most n + √ 2(n− 2) − 1 edges and we show this result is best possible with the correct order of magnitude on √ n. The 2connected case is also used to give a quick proof of Lai’s result on the general case. c © 1998 John Wiley & Sons, Inc. J Graph Theory 29: 11–?? , 1998