On super edge-magicness of graphs (Q2839695)

Given a graph \(G\), let \(p = |V(G)|\) and \(q = |E(G)|\). We call \(G\) edge-magic, if there exists a bijection \(\lambda : \{1,\dots,p+q\} \rightarrow V(G) \cup E(G)\) such that for every edge \(uv \in E(G)\) its weight \(w(uv) = k\) for some constant \(k\), where \(w(uv) = \lambda(u)+\lambda(v)+\lambda(uv)\). Such a labelling \(\lambda\) is called edge-magic total. If \(\lambda(v) \in \{1,\dots,p\}\) for every \(v \in V(G)\), then we call \(\lambda\) super edge-magic total labelling and every graph \(G\) for which such a labelling exists, super edge-magic graph. The authors use simple constructions to show that zig-zag triangles, disjoint union of a comb and a special comb, disjoint union of a star and a banana tree and disjoint union of stars are super edge-distance magic.