Strong edge-magic graphs of maximum size (Q924958)

A graph \(G=(V,E)\) is called strong edge-magic, a SEM graph, if there exist bijections \(\phi :\) \(V\rightarrow \{1,\dots,\left| V\right| \}\,,\) and \(\lambda :E\rightarrow \{\left| V\right| +1,\dots,\left| V\right| +\left| E\right| \}\) so that, for each edge \(e=uv\) in \(G\), \(\phi (u)+\phi (v)+\lambda (e)=k,\) for some constant \(k.\) It is know that a SEM\ graph on \(n\) vertices has at most \(2n-3\) edges. In this paper the graphs of this maximum size are studied.