On magic graphs (Q2725024)

An edge-magic labeling of a graph \(G\) with \(n\) vertices and \(m\) edges is a bijective function \(f\colon V(G)\cup E(G)\to\{1,2,\dots,m+n\}\) such that \(f(u)+f(v)+f(uv)=k\) is a constant for any edge \(uv\) of \(G\). Labeling \(f\) is said to be edge-antimagic if the values \(f(u)+f(v)+f(uv)\) are distinct for all edges \(uv\) of \(G\). The author introduces several variations of edge-magic and edge-antimagic labelings and exhibits such labelings for a number of classes of graphs. Also some open problems and new conjectures are raised.