On the super edge-magicness of graphs with a specific degree sequence

Abstract

A graph $G$ is said to be super edge-magic if there exists a bijective function $f:V\left(G\right)\cup E\left(G\right)\to \left\{1,2,\dots ,\left|V\left(G\right)\right|+\left|E\left(G\right)\right|\right\}$ such that $f\left(V\left(G\right)\right)=\left\{1,2,\dots ,\left|V\left(G\right)\right|\right\}$ 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 $s:4,2,2,\dots ,2$. We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems.