Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E(G), define d(e) = d(u) + d(v). Let F denote the set of all simple 2-edge-connected graphs on n ≥ 4 vertices such that G ∈ F if and only if d(e) + d(e’) ≥ 2n for every pair of independent edges e, e’ of G. We prove in this paper that for each G ∈ F, G is not Z
3-connected if and only if G is one of K
2,n−2, K
3,n−3, K
2,−2
+
, K
3,−3
+
or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 2010, 310...
