ON THE SIZE OF GRAPHS WITH ALL CYCLE HAVING DISTINCT LENGTH

Let f (n) be the maximum number of edges in a graph on n vertices in w hich no two cycles have the same length. In 1975, Erdos raised the que stion of determining f(n)(see Bondy and Murty(1976)). In this note, we prove that for n greater-than-or-equal-to 36.5t2 - 4.5t + 1 one has f (n) greater-than-or-equal-to n + 9t - 1. We conjecture that lim(f(n) - n)/square-root n less-than-or-equal-to square-root 3.