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...
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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 |
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| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/7/ |
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| author | Wai Chee Shiu Richard M. Low Andy K. Liu |
| author_facet | Wai Chee Shiu Richard M. Low Andy K. Liu |
| author_sort | Wai Chee Shiu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7c58bd438d384f2597f5ca33c17f2eaf |
| institution | Kabale University |
| issn | 2470-9859 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Georgia Southern University |
| record_format | Article |
| series | Theory and Applications of Graphs |
| spelling | doaj-art-7c58bd438d384f2597f5ca33c17f2eaf2025-01-15T17:45:21ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592024-01-0111110.20429/tag.2024.110107 Face-magic Labelings of Polygonal GraphsWai Chee ShiuRichard M. Low Andy K. LiuFor 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.https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/7/face-magic graph labelingpolygonal graphs |
| spellingShingle | Wai Chee Shiu Richard M. Low Andy K. Liu Face-magic Labelings of Polygonal Graphs Theory and Applications of Graphs face-magic graph labeling polygonal graphs |
| title | Face-magic Labelings of Polygonal Graphs |
| title_full | Face-magic Labelings of Polygonal Graphs |
| title_fullStr | Face-magic Labelings of Polygonal Graphs |
| title_full_unstemmed | Face-magic Labelings of Polygonal Graphs |
| title_short | Face-magic Labelings of Polygonal Graphs |
| title_sort | face magic labelings of polygonal graphs |
| topic | face-magic graph labeling polygonal graphs |
| url | https://digitalcommons.georgiasouthern.edu/tag/vol11/iss1/7/ |
| work_keys_str_mv | AT waicheeshiu facemagiclabelingsofpolygonalgraphs AT richardmlow facemagiclabelingsofpolygonalgraphs AT andykliu facemagiclabelingsofpolygonalgraphs |