The diameter of domination k-critical graphs

A graph is k-domination-critical if γ(G) = k, and for any edge e not in G, γ(G + e) = k ? 1. In this paper we show that the diameter of a domination k-critical graph with k ≧ 2 is at most 2k ? 2. We also show that for every k ≧ 2, there is a k-domination-critical graph having diameter (3/2)k ? 1]. We also show that the diameter of a 4-domination-critical graph is at most 5.