Face-magic Labelings of Polygonal Graphs - Wai Chee Shiu; Richard M. Low; Andy K. Liu (Theory and Applications of Graphs)
For a plane graph $G = (V, E)$ embedded in $\mathbb{R}^2$, let $\mathcal{F}(G)$ denote the set of faces of $G$. Then, $G$ is called a $C_n$-face-magic graph if there exists a bijection $f: V(G) → \{1, 2, …, |V(G)|\}$ such that for any $F \in \mathcal{F}(G)$ with $F \cong C_n$, the sum of all the vertex labels along $C_n$ is a constant $c$. In this paper, we investigate face-magic labelings of polygonal graphs.