New results on 3-domination critical graphs

A graph G is said to be 3-domination critical if its domination number γ(G) = 3 and γ(G + e) = 2 for any edge e not contained in G. In this paper we first establish some structural properties of 3-domination critical graphs with diameter equal to 3. In particular, this allows us to characterize a special family of 3-domination critical graphs which contains those with minimum degree one. Moreover, we show that if the minimum degree of a 3-domination critical graph G is at least 3, then α(G) ≤ κ(G) + 1 or G is superconnected, where α(G) is the independence number and κ(G) is the vertex-connectivity of G.