title: Graph theory problem, diameter and average pairs distance
body: <p>Claim : There exists a positive natural number c so that for all connected graphs G, it
  is the case that: (diam(G) / apd(G)) &lt;= c. </p>
  
  <p>This claim is false and we can show that for any c > 0, we can still construct a graph G such that (diam(G) / apd(G)) > c.</p>
  
  <p>But what if, </p>
  
  <p>Claim: There exists a constant c so that for any connected graph G, it
  is the case that: (diam(G) / apd(G)) &lt;= c. </p>
  
  <p>Could someone proof or give an counterexample? </p>