On domination number and distance in graphs

A vertex set SS of a graph GG is a dominating set   if each vertex of GG either belongs to SS or is adjacent to a vertex in SS. The domination number  γ(G)γ(G) of GG is the minimum cardinality of SS as SS varies over all dominating sets of GG. It is known that γ(G)≥13(diam(G)+1), where diam(G)diam(G) denotes the diameter of GG. Define CrCr as the largest constant such that γ(G)≥Cr∑1≤i