A graph \(G\) is said to be super edge-magic if there exists a bijective function \(f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}\) such that \(f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}\) and \(f\left(u\right) + f\left(v\right) + f\left(uv\right)\) is a constant for each \(uv\in E\left( G\right)\). In this paper, we study the super edge-magicness of graphs of order \(n\) with degree sequence \(s:4, 2, 2, \ldots, 2\). We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems.
