On \((a,d)\)-antimagic prisms (Q2715964)

A simple undirected graph \(G=(V,E)\) is \((a,d)\)-antimagic, \(a\) and \(d\) being positive integers, if one can label its edges by \(1, 2, \ldots , |E|\) so that \(\{s(v): v\in V\}=\{a, a+d, \ldots , a+(|V|-1)d\}\), where \(s(v)\) denotes the sum of labels of the edges incident with \(v\). The prism \(D_n\) is a trivalent graph consisting of two disjoint \(n\)-cycles \(1 2\ldots n\) and \(1' 2'\ldots n'\) and \(n\) edges \(ii'\). The authors characterize all triples \((a,d,n)\), \(n\) even, such that \(D_n\) is \((a,d)\)-antimagic. They give a partial result also for odd \(n\).