Edge-antimagic graphs (Q878610)

A bijection \(g: V(G) \cup E(G) \rightarrow \{1, 2, \dots , | V(G)| +| E(G)| \}\) is called an \((a,d)\)-edge-antimagic total labeling of graph \(G\) if the edge-weights \(g(x)+g(xy)+g(y)\) over all edges \(xy\) form an arithmetic progression with initial term \(a\) and difference \(d\). Such a labeling is super if \(g(V(G))=\{1,2,\dots,| V(G)|\} \). The authors calculate properties of \(a\) and \(d\) for which various families of graphs have such labelings.