ERRATUM to: Double domination edge removal critical graphs

In Section 5 of [1], class H2 should be defined as follows: Let H2 be the family of graphs whose vertex set contains a set D that induces a star K1,r (with r ≥ 1), of center vertex x and leaves x1, . . . , xr, such that: for every vertex u of V (G) − D, N(u) is equal to either {x1, x2} or {x, xi} for some i ∈ {1, . . . , r}; moreover, if any vertex z of V (G)−D satisfies N(z) = {x1, x2}, then no vertex u of V (G) − D satisfies N(u) = {x, x1}. In [1] the proof of Theorem 18 (p. 298, line 4), the clause “all remaining vertices of V (G) − D are either xl, xl′ or to x, xl” must be replaced by: then we may assume, up to symmetry, that no vertex u of V (G) − D satisfies N(u) = {x, xl′}.