Ore-condition and \(Z_3\)-connectivity (Q942129)

Let \(G\) be a simple graph of order \(n\geq 3\) such that \(d(x)+d(y)\geq n\) for each pair of non-adjacent vertices \(x\) and \(y\). Then the authors prove that \(G\) is \(A\)-connected for any abelian group \(A\) with \(|A|\geq 3\) if and only if \(G\) is not one of 12 completely described graphs of order between 3 and 6.