The connection between the magical coloring of trees
Let $ f $ be a set-ordered edge-magic labeling of a graph $ G $ from $ V(G) $ and $ E(G) $ to $ [0, p-1] $ and $ [1, p-1] $, respectively; it also satisfies the following conditions: $ |f(V(G))| = p $, $ \max f(X) < \min f(Y) $, and $ f(x)+f(y)+f(xy) = C $ for each edge $ xy\in E(G) $. In thi...
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AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241354?viewType=HTML |
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| author | Jing Su Qiyue Zhang Bing Yao |
| author_facet | Jing Su Qiyue Zhang Bing Yao |
| author_sort | Jing Su |
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| description | Let $ f $ be a set-ordered edge-magic labeling of a graph $ G $ from $ V(G) $ and $ E(G) $ to $ [0, p-1] $ and $ [1, p-1] $, respectively; it also satisfies the following conditions: $ |f(V(G))| = p $, $ \max f(X) < \min f(Y) $, and $ f(x)+f(y)+f(xy) = C $ for each edge $ xy\in E(G) $. In this paper, we removed the restriction that the labeling of vertices could not be repeated, and presented the concept of magical colorings including edge-magic coloring, edge-difference coloring, felicitous-difference coloring, and graceful-difference coloring. We studied the magical colorings on the tree and proved the existence of four kinds of magical colorings on the tree from a set-ordered edge-magic labeling. Further, we revealed the transformation relationship between these kinds of colorings. |
| format | Article |
| id | doaj-art-bbefe256e32c450b9f9895c307dcce19 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-bbefe256e32c450b9f9895c307dcce192025-08-20T02:08:44ZengAIMS PressAIMS Mathematics2473-69882024-09-01910278962790710.3934/math.20241354The connection between the magical coloring of treesJing Su 0Qiyue Zhang 1Bing Yao21. College of Computing Science and Technology, Xi'an University of Science and Technology, Xi'an 710054, China2. College of Ulster, Shaanxi University of Science and Technology, Xi'an 710016, China3. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaLet $ f $ be a set-ordered edge-magic labeling of a graph $ G $ from $ V(G) $ and $ E(G) $ to $ [0, p-1] $ and $ [1, p-1] $, respectively; it also satisfies the following conditions: $ |f(V(G))| = p $, $ \max f(X) < \min f(Y) $, and $ f(x)+f(y)+f(xy) = C $ for each edge $ xy\in E(G) $. In this paper, we removed the restriction that the labeling of vertices could not be repeated, and presented the concept of magical colorings including edge-magic coloring, edge-difference coloring, felicitous-difference coloring, and graceful-difference coloring. We studied the magical colorings on the tree and proved the existence of four kinds of magical colorings on the tree from a set-ordered edge-magic labeling. Further, we revealed the transformation relationship between these kinds of colorings.https://www.aimspress.com/article/doi/10.3934/math.20241354?viewType=HTMLset-ordered edge-magic labelingmagical coloringtree |
| spellingShingle | Jing Su Qiyue Zhang Bing Yao The connection between the magical coloring of trees AIMS Mathematics set-ordered edge-magic labeling magical coloring tree |
| title | The connection between the magical coloring of trees |
| title_full | The connection between the magical coloring of trees |
| title_fullStr | The connection between the magical coloring of trees |
| title_full_unstemmed | The connection between the magical coloring of trees |
| title_short | The connection between the magical coloring of trees |
| title_sort | connection between the magical coloring of trees |
| topic | set-ordered edge-magic labeling magical coloring tree |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241354?viewType=HTML |
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