Size in maximal triangle-free graphs and minimal graphs of diameter 2

A triangle-free graph is maximal if the addition of any edge creates a triangle. For n ~> 5, we show there is an n-node m-edge maximal triangle-free graph if and only if it is complete bipartite or 2n-5<<.m<<.L(n-1)2/4J+l. A diameter 2 graph is minimal if the deletion of any edge increases the diameter. We show that a triangle-free graph is maximal if and only if it is minimal of diameter 2. For n> n o where n o is a vastly huge number, Ftiredi showed that an n-node nonbipartite minimal diameter 2 graph has at most [_(n-1)2/4J+ 1 edges. We demonstrate that n o ~> 6 by producing a 6-node nonbipartite minimal diameter 2 graph with 8 edges.