Face-magic Labelings of Polygonal 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 \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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Georgia Southern University
2024-01-01
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| Series: | Theory and Applications of Graphs |
| Subjects: | |
| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/7/ |
| Summary: | 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. |
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| ISSN: | 2470-9859 |