@article{Su2024, 
author = {Jing Su and Qiyue Zhang and Bing Yao},
title = {The connection between the magical coloring of trees},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {27896-27907},
keywords = {set-ordered edge-magic labeling, magical coloring, tree},
url = {https://www.sciopen.com/article/10.3934/math.20241354},
doi = {10.3934/math.20241354},
abstract = {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,  maxf(X)<minf(Y), and  f(x)+f(y)+f(xy)=C for each edge  xy∈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.}
}