Face-magic Labelings of Polygonal Graphs

Authors

Wai Chee Shiu, The Chinese University of Hong KongFollow
Richard M. Low, San Jose State UniversityFollow
Andy K. Liu, San Jose State UniversityFollow

Abstract

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 \textit{$C_n$-face-magic graph} if there exists a bijection $f: V(G) \to \{1, 2, \dots, |V(G)|\}$ 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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Shiu, Wai Chee; Low, Richard M.; and Liu, Andy K. (2025) "Face-magic Labelings of Polygonal Graphs," Theory and Applications of Graphs: Vol. 11: Iss. 1, Article 7.
DOI: 10.20429/tag.2024.110107
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/7